I'll addresss changes that would improve gameplay, and not surprisingly a lot of them point to getting back into the spirit of of Fallout 1/2 just a bit more. Bethesda has my full permission to take and use, or adapt any of these ideas for use going forward.
The primary problems of the game can be broken down into SPECIAL, the skill system, startup Traits, maximum level, Action Points, and just a general lack of weapon/armor variety. These are all interrelated to some degree and I'll explain what's wrong with them, and how I'd go about fixing them.
S.P.E.C.I.A.L isn't
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While you adapted the lettering, and the concept, the fact is that the SPECIAL stats don't have a strong enough impact on the game and are completely overshadowed by Skills by the time you hit level 5. So what is good in concept ultimately becomes watery flavor. Stats need to mean more! The best, cleanest, and easiest way to do this within your current system is this:
--> Change the skill system to a max learned rank of 50, and have the other 50 points derive from the relative stat at 5 skill points per SPECIAL point. This means that a character that torpedo's a stat to 1 will have a maximum skill rank of 55 (which is an acceptible, if not great level), while a character with 10 points caps out at 100 and STARTS at 50 making them a natural at those skills.
--> Bigger carrying bonus per point of Strength (so that people that torpedo it will feel the hurt, while those who go high feel that it's worthwhile even before Strong Back)
--> Perception should be increasing chances of a crit... knowing where to hit, and anticipating how your opponent is going to present an opening, etc.
--> Endurance should reduce chances of a crit against you as well as increase your HP.
--> Charisma doesn't need to change a great deal as long as the skill system is in place, since high Speech skills will be available to only those with high Charisma.
--> Intelligence is fine, though the number of skill points per level should be 2 + INT (or maybe 4 + INT/2) given the lower number of skill points required to max.
--> Agility should be increasing accuracy, perhaps running speed, and reducing chances to be hit. It probably should NOT modify action points because that makes it too good.
--> Luck is basically fine as-is... add 1 effective (stat-based) Skill point per unit of luck, still increase crit chance.
The Skill System
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The basics were already covered under SPECIAL... there are too many points floating around and too easy to completely dwarf the impact of Stats, which makes them meaningless. Reducing the maximum learned level of skills and reducing the rate of aquiring skill points will make skills more interesting and each point mean more. As a side effect, gear that gives stat bonuses and Perks that provide bonuses are inherantly better.
By making SPECIAL impact skills to a greater degree, Intelligence isn't quite the must-have that it is now, which encourages greater character variety and enhances replayability, which makes the game a better deal for players, will increase game longevity, and keep players from wanting to sell their used game since they can play through a dozen times with different tactics and get very different results.
Background Traits
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These were removed from Fallout 3, and apparently just incorporated into Perks. I suppose this is partly because you wanted to show everyone growing up as background instead of picking things. However, Background Traits greatly increased replayability and need to be reinstituted. Some of the crappier Perks should be reconstituted as Background Traits, and others added.
Examples:
--> Lead Belly: Food healing is increased by 50%, radiation from food is decreased 75%, but Stimpacks are only 40% effective.
--> Cannibal: Eating a corpse increases your HP by 20% of maximum, but you suffer a karma penalty and have a 10% chance of an interruption of dialog as people become unsettled with the way you look at them (overcome with a speech check.)
--> Nerd: +10 Science, +5 Repair, -2 Charisma
--> Injured: -10% movement speed, +15 Speech bonus (sympathy points)
--> Sweet Talker: +20 Barter and Speech with members of the opposite six. -10 Barter and Speech with members of your six
--> Hot!: You must keep your radiation levels between 600 and 1000 or else you suffer from radiation penalties. Anyone who hits you in melee combat takes 10 damage.
--> Quick Draw: Switching weapons in combat only costs
Maximum Level
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As should be apparent by this point, people resent being told that they're as powerful as they're ever going to get. This is a single player game... it doesn't hurt anyone to give people more to look forward to. The Achievers need advancement to feel fullfilled, so capping people is a bad idea. What you could do though is dramatically reduce levelling perks as well as start jacking up the XP required to do it. This would also make Swift Learner a better Perk.
--> At level 20, the Int and Perk bonus to skill for levelling goes away. (ie. 3 per level flat) Reduced HP gain per level (flat)
--> At level 25, the base skill per level decreases to 2. Further reduced HP gain per level.
--> At level 30, the base skill per level decreases to 1. 2 HP per level.
Action Points
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Overall, it's well done. However, there are a few flaws... Agility probably shouldn't increase this (or else it becomes too useful) and it'd probably be a good idea if Skill with the weapon decreased the base # of action points required somewhat, so that people skillful with small arms can squeeze off an extra round, or people with high Unarmed skill can really lay down the blows.
The biggest problem though is that bringing up the PipBoy to change weapons or activate a stimpak really needs to cost action points (in VATS mode) or time in normal mode (have everyone else move at 25% rate while you have it up, don't stop time.) Perks could modify the time cost of using the PipBoy
Gear Variety
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It'd just be nice to see different guns, armor, etc, with various stats... document range penalties/spread, action point costs for use, etc.
Summary
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The engine is close.... with a bit more tweaking, it could be great. Fallout 4 could blow us all away... I'd love to see it.