Two notes: this is long, it is based entirely on the idea that I have limited time and budget, and so I can only do so much, while still being expected to deliver the animation improvements Todd Howard alluded to, fresher graphics, and some sound control upgrades.
Speechcraft would be entirely replaced with two-track system. The first track simply gives a few stock options for each of the speech categories present in Oblivion, and you use those boasts, threats, jokes, and compliments to attempt to make people like you. It will give you the magic 100 disposition, but much slower than Oblivion. The second track allows you to earn and learn new options, whether it be a joke the local smith tells, or some old flattery from a Bosmer love poem. These options tend to receive much larger disposition swings in one direction or another, and may require extensive effort to get (on an individual basis). Of course, some of these options are going to fall in your lap through books or normal dialog.
Speaking of dialog, I would resurrect "Streetwise" and "Etiquette" as arrows on a Fallout 3-style dialog menu. Basically, you enter conversation in "casual" tone. To complete the game, you should never be FORCED to change, but it certainly is easier and more fun to use the left and right arrows. (Left -> Streetwise/blunt, right = etiquette/polite). You can change tone at any point in conversation, and the last setting you used is remembered. So... suppose you accidentally choose "blunt" speech... the game should not demand you figure out to press right once to move on. It's just a choice that may or may not earn you funny lines, unique options, and unexpected responses. Or maybe a character just doesn't care, and replies to all speech the same way. It depends on the NPC.
Mercantile: this should level according to several factors, but primarily the item's value, what you sold it for, and the maximum you could have based on skill and disposition. Also, getting higher values from skill 5 merchants is less valuable than hammering out a somewhat reduced value from a ruthless Master merchant... to a point. An actual living economy would likely prove too involved for one game to implement well alongside much of what I wish to accomplish, but it would be conceivable to implement certain stubs that would allow mods to, for example, control the merchant's overall gold and allow for the random buying and selling of items (as well as allowing mods to decide whether unique items, quest items, and artifacts may be sold to NPCs... although these would invariably need to stay "in circulation" within the province). But a living economy would not be a primary focus on the basis of "I have a lot of other things I want to do, and I can't have it all."
Magic: Spell tiers are gone, in favor of individual spell levels. Magicka cost replaces constant increment for leveling. Fortify effects are dramatically nerfed, while striving to make underused spells more worthwhile. In addition, there would be a spell efficiency field, which allows for two spells of identical effect to be different on the basis of one is the wasteful spell of a novice, while the other is the sure, practiced hand of a master. Custom spells would start the game as incredibly inefficient novice spells (at minimum skill) and work their way up to something between "standard" and "very efficient". Most efficient of all, and most powerful (usually) would be "Legendary Spells". These spells would be rare, usually powerful and efficient, but count as a boast, besides being most likely useful. Think "Finger of the Mountain", only done right (ie, cost lower than auto-calculate could do). Low priority stuff that might not see use in-game, but I'd like to offer for mods: up to five scripted spell failures per spell and the ability to register a spell success callback for magicka-based skill mods to go into the realm of leveling individual effects.
Archery: record shot distances. Make long-range shots worthy of a speechcraft boast.
Hand-to-hand: add brass knuckles and punch dagger type weapons. Set up local contests of pugilism. Not particularly interested in using too much development time to make alternate animations just to please people who want alternate combat styles this time around.
Armorer: in some way, shape, or form, this skill needs to be made lore correct. This one? I have no bright ideas, so I would offer a developer bounty to anyone who finds a way to make it happen.
Alchemy: fix the few bugs present in the Oblivion equations, and hope to add a potency measure to each effect of each ingredient. That way, different combinations could have different effects. Also, the choice between making a poison or a potion when a combination has good and bad effects.
Security: I'd re-introduce trapped locks, but make the whole process multistage and requiring far more than a pick and a probe to unlock several chests. As with many other decisions, I expect to take some fire from the fanbase for making these traps appear mainly on chests that are quite optional to open. But then, I'll also make such chests the kind you'd naturally feel compelled to peek into by sheer curiosity. Sometimes, I'd even reward you. (Yes, I'm the kind of jerk who might well put one of the hardest trap and lock combinations on a chest of... worthless dinnerware).
Sneak: aside from making rooftops somewhat more viable for an acrobatic type, I doubt I would change much. Sorry, stealth-lovers. I know you want more. Take consolation in the fact that I'm about out of systems I want to remake more!
Enchantment: people want the skill back. Sorry. A complete mechanics overhaul is in order this time around. Essentially, the process should offer numerous soul sizes (Morrowind), but without the numerous headaches associated with that freedom. This can be done simply by binding 1 soul to 1 effect, and letting the user choose the parameters (ie, cast on use/strike or struck/constant effect, radius, magnitude, and duration). Not all options are always available (duration and for all but a few effects, radius are meaningless to constant effect, etc). Multiple enchantments couldd then be achieved, although the maximum enchantment value would be less than 2 high-class souls, which limits the number of strong effects one coul have.
Leveling: The system will now store how many skill increases you gain for the whole game, get rid of the multiplier system, and instead offer you a maximum of 20 points and a minimum of 1 to distribute according to what you've done. Suppose I decide to master Hand-to-Hand, Conjuration, Sneak, Acrobatics, Illusion, Alteration, and Alchemy all while at level 1. That would probably equal out to a lot more than 20 points of stat increases. What I can't do is dump everything into Endurance. What I can do is dump most or all of it into personality, because I did a lot to increase it. Endurance would be very lucky to see 2 points.
Mod-related: lists now also include "Append lists" and "Delete lists", to make mods work together better. I'd also have the scripting team look at highly popular mods that pull sheer script abuse to achieve an effect that could be made simpler through including OBSE extensions natively, or by adding new features, or by exposing a bit more of the game to scripts. Basically, most mods can probably be simplified, but we care most about the ones that require a grandmaster of scripting, OBSE, and heaps of extra work and are still almost profane in the steps necessary. Because if we like it, we should be trying to find places where thirty lines of script could be replaced by a few lines using a new operation.
The writing side? Foremost, execution of pre-planned storylines. Make sure everything is done as right as possible, attention to detail, and preferably at least a few points where you can take more than one route to a plot point.
Second, new books everywhere. The old ones will largely have any skill increases removed, but they will be retained. They're just retired from their previous importance (though not value).
Multi-part quests (wasteland survival guide from FO3) and long duration quests (The Ultimate Heist) need to return, as do complex affairs like "Whodunit?". These all offer either replay value, or a sense of accomplishment.
Also, I want the player to be overwhelmed by some places in the game. There's an entire history to the province. If the players who read in-game books don't stop and go "OH MY GOD! THIS IS WHERE..." at least five times in a play through, we've failed to bring that history to life. Name a province, and someone can probably reply from memory at least one place they'd like to see, and post a half page of solid text or more about the feel. Example: I want Solitude to look and feel like a grand city, but as you explore it, have it be, as a customer at work once described a nearby branch, "spiritually dark". Potema's reign left scars on the populace, and it is mortal nature to pass on scars, if by different means.
Likewise, "Wabbajack" tells of a library. I want to see it, and where a man could have been under it. There should be a place that maybe seems unimportant, but when a thunderstorm hits, it should take on a different, tormented air. This would be where a young Pelagius summoned Sheogorath, thinking he was getting Herma-Mora. If that made the game, and you caught on, you couldn't help but go "this is where!"
I want quests where rushing in leads to tears for you, because all is not what it seems. Lies should be told, both directly and indirectly. Sometimes, the fellow who is obviously dirty should still be the lesser evil. I want dungeons that are so large that with a 10000 unit feather spell, you can't clear it out with 500 strength, and I want a non-quest reason to explore it. Not for reward, but simply that the game makes me want to delve through a massive underground complex. I want quests where you are being double- and triple-crossed in a shadow war between overtly friendly factions (merchants, houses, families, whatever).
The Dark Brotherhood and its ilk need to do some truly unjust things. If there's one thing that stands out about the Dark Brotherhood aside from the Traitor segment in Oblivion, it's that the only quest you have a reason to feel guilty about is the Draconis family. Nothing else ever made you feel a moment's regret. Being an assassin should involve some gut-wrenching wrongs, done by your hand.
The Fighter's Guild... I hope Keyes kills it, as with the Mage's Guild. Through three games, I have yet to like these people. They act all tough, and they're either corrupt bastards or sissies in need of a lot of training. Either way, I'd rather disband it and start fresh than deal with the history. So, I propose the formation of a "Brotherhood at Arms" that handles monster hunting and private security tasks. No one will ask you to join, unless you've done a quest that is scripted to make them take note. These guys still pay service to the law, but they aren't shy about asserting their influence with a little pugilism out behind the local watering hole. So, basically, these guys are not the friendly Fighter's Guild of Oblivion, but a group that grants respect grudgingly. They train hard, fight hard, drink hard, and wench hard. Respect, with them, comes from results. However, they crack down on their own ferociously as well. The occasional B&E or small theft doesn't bother them at all. Large thefts do... if it's proven. Assaults on members without sanction (ie, if you are not conducting "internal discipline"), murder, [censored], and banditry are all cause for discipline. Fighting back during disciplinary actions is also a no-no. So don't be bad!
I don't think the guilds need to have a major conflict, but it would be nice if certain guild quests needed a complex and involved solution to avoid infuriating a Guild you might be a member of.
There would be quests from both the Gods and their Priests, and the Daedric Princes and their cults. You'd have to serve the cult before the Prince, and it would take more than one quest to gain divine or Daedric favor.
In addition, there should be a small number of class-linked quests. When walking past a quest-giver, they would stop you if you are of the right class. Otherwise, you need a degree of reputation (good, bad, or total) and a certain degree of skill before you can bring it up in conversation. Custom classes suffer slightly, as they have only the standard free quests.
In general, there should be more quests that require reputation and skill, and quests should involve more stages. I hated the Morrowind quests that could be solved by walking 500 feet, talking to someone, and walking back. Maybe with 1-2 enemies killed in between. Some quests should be simple, but some of the steps need not be. For example, a delivery quest could have a time limit, or otherwise be to an obscure place. That would force you to either rush or spend time seeking out a well-hidden location to complete the quest. Either one is an upgrade.
About Quest markers and the compass: The compass itself stays. Markers for undiscovered locations would only appear under a narrow set of conditions. First, if you've had a direct line of sight to the place from somewhere. You know about where it is, and it appears as a defined undiscovered place on your map, just like if someone marked it for you. Second, I would derive a perception stat from skills and stats, and this would automatically detect places in a relatively small radius as "suspected place" with a ? icon. Third, the above ability could be enhanced by Mysticism spells to increase range, and at high levels, give a place type inside the perception range. Fourth, there can eventually be a compass upgrade that is enchanted, and returns the compass to Oblivion-style functionality. But at least now it's explained!
Quest markers would be available, but not as a GPS device. The basic idea is that if you know a city is "south", it just puts the arrow on the exit to your city. When someone gives you a marker, it gives you a marker to keep you oriented. Essentially, just guiding you to a known place. For people, it guides you to the city they are usually in, unless you've met them, in which case, it leads you to their last known location, unless you know they have a home or business. Then it will direct you there. Scripted exceptions are made for characters with an intended schedule (if you have the schedule in-game): this produces one or two locations. One is where they "should be", and if there are two, the schedule says they are traveling. One for origin, one for destination.
As far as fast travel goes, I'll take no action beyond anything the staff agrees is needed, because there's no single solution. Going back to exactly what Morrowind had isn't going to happen on my watch (why should I have to manually select four boats to reach my destination, when I've used all of the routes needed?), and people whine about Oblivion (but are much more OK with the same system in FO3). So I'll punt this one to the staff.