Your reason for locating your father is absolutely believable-- you want to know why he left, learn whether there is any truth to what Moriarty tells you (in regard to you being born in the vault being a lie and as to what else may be a lie) and you have nothing for you in the Capital Wasteland. You know nothing about the outside world, have no friends, food, shelter or water-- it seems like finding your father would be a pretty big priority, especially considering you've been reliant on him your entire life-- the very same life which up until the vault doors closing behind you has been easy street. Truth is, locating your father may very well be the only reasonable objective at that point in time. Even someone who hated his father would very likely seek him out at that juncture, with due consideration.
You make my point for me. You know nothing about the outside world, so you're compelled to hunt your father down by trekking through increasingly dangerous missions and locations? That's ridiculous. You're a kid from a vault, you have no combat training.. how exactly is it reasonable for your character to want to throw his life away just to get answers from daddy?
The only reasonable objective? How about not dying? That's the primary objective that would come straight to my mind. "Well [censored], dad got me booted out of my home into a hellhole, now I can... A. Try tracking him down and get myself killed by raiders and super mutants, because all I have is a low caliber pistol that I've never used before today. Or B. Stay in Megaton and try to make a home here." I'd go with B. That's just me, obviously, and maybe a kid fresh out of a vault wouldn't put living very high on the priority list.
As for illogical missions, your father has no idea what is what since leaving the vault (as Three Dog explains). The water purifier may have been a weak plot device (it is certainly a lot stronger than a poker chip however, I'm not sure how that can even really be argued) but the Fallout universe has done anything but stick to accurate science (the G.E.C.K. being the most obvious example), not to mention their technology is entirely different, being tube-based primarily and everyone driving a nuclear powered car-- how does the fact that the water is still radiated not seem plausible? There could a dozen different reasons for that body of water being contaminated (an atom bomb sitting at the bottom of the body of water, high radiation levels from the subway contaminating the water table, so forth and so on). Also, keep in mind, James' intent with the water purifier is to create a fresh water source for everyone. There is quite a bit of purified water around the Capital Wasteland but many people do not have the means of obtaining it, their water purification systems are falling apart (Megaton) and people are killing each other on a daily basis over those water sources.
You're not sure how that can be argued? I'll demonstrate how. The difference between the fail MacGuffin of Fallout 3 (the water chip from the G.E.C.K.) and the awesome poker chip of New Vegas is that one makes sense in its own context and the other does not. I'll agree that suspension of disbelief will get you a long way, for example the advanced robotics without microprocessors. That isn't the problem. The problem is that within this setting, using a GECK this way still doesn't work. If you try to use the GECK in vault 87, if explains that using the GECK will be fatal to you because it will act as a kind of fertility bomb, rearranging all surrounding matter into a new, fresh landscape. Isn't that a more important use? Isn't breaking a GECK for a water chip kind of... stupid? Yes, yes it is. Further, all this chip grants (in theory, they hadn't tested it) is a source of clean water to the locals in a very low population zone on the east coast.
Perhaps if there isn't enough clean water to live in the capital... leave? Find somewhere with more clean water? Considering it is unlikely any location in the world took as many nukes to the face as D.C. did, they could just pick a direction and start walking and have better water. Maybe take that GECK with them and use it for its intended purpose and not break it with a hammer for one part? No, no, that would actually make sense.
Let's now look at the platinum chip. The chip is actually introduced early, but is not the central driving force of your interest in the plot (thus, it is not a MacGuffin), so it doesn't feel like a contrivance. The driving force behind the plot is first revenge/curiousity, and then politics and choosing a side in the imminent clash. The platinum chip is far more sensible as a plot device because they explain what it does and why it's important, and the explanation is actually reasonable.
It isn't a magical savior device, like in Fallout 3, but it is an item of immense importance to one man, because it vastly increases his grip on the region. This actually makes sense, especially considering the second half of the plot is a struggle for power between several factions. So it serves as both an adequate reason for someone to shoot you and a very good way to thread act one and act two together in the narrative. This logic actually works, and the writing behind it actually got some thought. Robert House designed the chip, was unlucky, and now is willing to do nearly anything to attain the key to fulfilling his plans. So in every way I can think of, the platinum chip is a far, far better story device.
Oh, and you don't have to BREAK A GECK to get it. Just saying.
This I mostly agree with. Please understand I'm speaking purely from a perspective relating to immersion. I don't understand what your motivation would be if not revenge initially however. You want to find the man who shot you in the head and have a friendly chat? I also do not agree with necessarily having to care who shot you. Your average person in the Fallout universe seems to murder no less than ten people before breakfast (usually over really mundane objects such as collectible bottle caps, nuka-cola or tin cans). Seeing as you've lived in the wasteland your entire life, there is no way for you to not rationalize this-- you'd have to be well aware of it.
That isn't the impression the Fallout universe leaves as a whole, it's the impression Fallout 3 leaves. There is a lot of killing in New Vegas, but there are far more peaceful quests and usually the "good" factions will actually need a good reason to kill someone.. badly programmed reactions to stealing a pencil notwithstanding.
I will concede the fact that you need to take that leap of faith to play the game (or any game) but for me, personally, the plot was done in such a contrived fashion so early that I'm having a really hard time becoming svcked into the adventure. Fallout 3 at least established suspension of disbelief. New Vegas has a hard time with it throughout.
This is not to say I dislike New Vegas entirely. At its core, it's still a fun game with some interesting quests but I don't think it's really better than FO3. Some of what it does well has to be taken for granted to even provide a refreshing experience from FO3 (such as crafting or hardcoe mode). While it succeeds in some areas as compared to FO3, it fails in others. I definitely do not believe it is so good that it's worthy of the praise it receives (especially from people who aside FO3 as garbage) but yes, I agree-- that much is subjective.
The leap required for Fallout 3 is far, far larger. You have to just wave away huge, huge flaws in logic that are throughout both the story and the setting (no sources of food, for example) to enjoy Fallout 3. Once you do, you also have to wave away bad dialogue, and the fact that there isn't even much of the bad dialogue around to find. After you do that, everything is peachy and Fallout 3 is awesome... but those are some big hurdles to jump.