Certainly, Fallout 3's depiction of a world 200 years after a nuclear war is in no way unrealistic, even disregarding the science-fiction elements like energy weapons and super mutants. Really, in many ways it would indeed be more plausible to say it was 200 years after the nuclear war, but I suppose Bethesda wanted to set it later than earlier games so that they could market it as a sequel, and so that the Enclave could be in it. However, it's important to note that Fallout has never been about creating a realistic vision of post apocalyptic life. The fun thing about fiction is that it doesn't have any obligation to be realistic. While certainly, some works of fiction will make an effort to be as realistic as possible, and make this a major selling point, other works will often do unrealistic things for the sake of artistic license, perception, entertainment, budget, or censorship. In the case of works set in science-fiction or fantasy worlds, this is especially excusable, and in fact audiences may find it more jarring if they break their own laws than reality's, even if their laws seem completely stupid if you apply real life logic. This can be especially true for video games, as whereas movies or books can get by just telling good stories, video games need to have fun gameplay, plus since the stories of many games are just use as an excuse for your character to kill lots of enemies anyway, the plot doesn't even have to make sense. Therefore, there are certain http://tvtropes.org/pmwiki/pmwiki.php/Main/AcceptableBreaksFromReality in games, and some unrealistic aspects of Fallout 3 can be excused because of this.
First off, technology working after 200 years. While realistically, prewar items that have not been used for 200 years wouldn't work, the game wouldn't be nearly as fun if you if it were like this. After all, you'll probably note that in Fallout 3, no one is making laser guns, assault rifles, miniguns, or any of those other things, so all the guns you find have probably been around before the war, though the ones being used by people have likely been restored by the people using them, if prewar weapons didn't work, the players' arsenal would be restricted to whatever weapons people still make (which in Fallout 3's case, appears to be limited to the ones you can create from schematics.) and maybe a few weapons that don't have any complex moving parts. Also, then you wouldn't be able to find hidden caches of prewar weapons or anything, which would make exploring feel less rewarding. Of course, this is just in regards to weapons, as to other technology, if all robots had stopped working, that would remove one entire category of enemies from the game, and if various prewar machines weren't working, that would mean less options for the player, as you couldn't do things like hack a terminal to deactivate turrets protecting a place, or repair prewar mechanisms and use them for your own purposes. The lights on the other hand are probably just still working so that many locations don't become completely dark.
As to ghouls, while radiation won't do that to you in real life, it does in Fallout, ghouls were around in earlier Fallout games and they still worked that way, after all. One thing that must be noted is that Fallout was never meant to be a vision of a future that would be plausible to modern people. Instead, it's heavily based on a '50s vision of the future, that's why computers look primitive compared to what we use now (People in the 1950s wouldn't have anticipated the advancements in computer technology made in recent years, after all.) why you see all those giant mutated insects, and why Three Dog never plays any music made later than the '50s on the radio. If you watch '50s science-fiction and horror movies, you'll probably note that radiation causing mutations in a normal creature is a common explanation for the monster, especially in B movies (In which, incidentally, the giant ants and scorpions would be pretty at home.) of course, now we know that radiation is more likely to kill you than turn you into a Hollywood monster, but at the time, the average populace didn't know all we know about radiation, and I'm sure the whole fear of nuclear war also made anything with words like "atomic" or "nuclear" get people's attention very easily. If you apply modern science to it, radiation producing ghouls would seem unrealistic, but from the perspective of someone in the 1950s, it might seem quite acceptable.
In regards to the wasteland, Bethesda probably wanted to convey the feeling of desolation, and felt that living plants would go against it. Personally, I feel that a skilled artist could still get the point across without making the wasteland look completely lifeless.
As to baseball, who is to say that no one plays it anymore? There are baseballs all over the place, baseball bats, baseball gloves... and it's not like all prewar knowledge vanished the moment the balls fell. It seems plausible that all those people who seem to be trying to make postwar life like prewar life again could decide to play it.
If i'm not mistaken the food had someting in it that gave the food a 200 year shelf life.
That handwave fails to explain why it hasn't already been eaten by hungry wastelanders well before you come by. it's not like the prewar food in the game is kept sealed and locked away in some hidden place that no human has set foot in before you, most of it is lying in plain sight on the shelves of supermarkets, or in refrigerators, if it was still good to eat, someone would have eaten it already. Keep in mind of course that since none of the facilities that produce these foods are active anymore, the supply of it is limited, so even if there aren't enough people around to eat it quickly, over time it will inevitably all be consumed, or it will reach a point where even Science! can't keep it edible, whichever happens first.
If all the plants die, then there's no seeds to bring the plants back.
If all the plants die, there's also no plants to produce more oxygen for people to breathe, SO EVERYONE WOULD DIE DUE TO THERE BEING NO OXYGEN TO BREATHE. In other words, there are still living plants somewhere, and no just in Oasis, that's not enough to support human life everywhere
Spoiler Besides, it seems like the trees only started growing recently after Harold got there, yet people still had oxygen to breathe before that.
Even if all the plants in the Capital Wasteland had died, the seeds from other plants in other places where thast didn't happen should have spread to the Capital Wasteland after 200 years.
Wait, what? Would you please sneak into Chernobyl (since it's still a sealed-off area), without any suits on but your mere clothes and stay there for a week? Then after a year, after you feel the results of the radiation tell us how you think about it? Chernobyl is still heavily irradiated mate.
It's still heavily irradiated, of course, but it hasn't been two hundred years since the Chernobyl disaster, but what happened in Chernobyl is very different from what happened in Fallout 3. In Chernobyl, it was a nuclear reactor that exploded (and not in an explosion like the bomb in Megaton, mind you, despite what some fiction wants you to think, nuclear reactors aren't nuclear bombs, and a nuclear reactor related disaster will not produce the same results as a nuclear bomb.) aside from the fact that the reactor was designed to be a reactor, not a bomb, the radioative materials used in Fallout's nuclear weapons were likely different from what was used in the power plant, and the radiation released by them would also likely not last for the same amount of time, calling the nuclear war in Fallout 600 Chernobyls exploding all over the world is a pretty inaccurate description.
It must be remembered that, as has been said, nuclear weapons are designed to
flatten cities, meaning, produce a really large explosion, they also produce a large amount of radiation, but that's because of how they work, it generally isn't their main function, bombs are, after all, usually made to blow stuff up.
Some people play this game because it's kinda like Oblivion with guns. (They're the ones who want to import every single COD game and Counterstrike as well).'
Some people play it because they like Fallout.
And some people play it because they just like good games and don't care what it's labeled as or what games it resembles.