The big Problem with 3 versus New Vegas and by relation also 1 and 2 is pretty much just the lore. As well as quite a few Gameplay Decisions and Storylines.
The FEV (Forced Evolutionary Virus) was started as the PVP (Pan-Immunity Virion Project) which was initially designed to literally grant immunity against any kind of biological or chemical Weapon. You can already see that this didnt turn out well. Instead of having the desired Effect it instead created literal Super Soldiers, albeit it also made them much more aggressive. The Project was given to West Tek who developed it internally for a few Years, in part because of increased Tension with China, as well as to prevent another Outbreak of the "Plague" which swept the Nation previously, killing Millions. Due to the shift of the Research is was moved to the Mariposa Military Base for further Research and Testing. When the War broke out, West Tek was one of the Targets directly hit by one of the Nuclear Missiles fired by either side, who did it nobody really knows. The FEV got into the Atmosphere and basicly mixed with the radiation, making the Survivors largely immune to direct Contact with it.
Which was the sole Reason the Master later wanted completely clean Humans to turn into his Super Mutants, which he thought were the next logical Step. Remove anything making Humanity different and start from scratch. The Idea was rather noble on Paper, but FEV also made the Super Mutants sterile, meaning that if everyone was turned, we'd eventually die out.
Research of FEV was NEVER passed to a Vault, which while being designed as Scientific and Sociological Studies by the Enclave, the Enclave would never introduce a experimental Virus or mutagenic Substance to any one of them because it would essentially ruin everything, especially because it'd have disastrous Results. The White Noise System tested in another Vault is more likely to happen, as it can be kept local and if failure is apparent, terminated, or at least wont be a viable Threat in the future. Therefore, Super Mutants in the Capital Wasteland are illogical, they COULD have come from the West, in fact, the Storyline would suggest that easily, in that the Super Mutants fled east after the Master died, but they couldnt create more, as by that Point, Mariposa was in ruins and they couldnt simply create more FEV out of thin air.
The Enclave making a return is also another big Problem, especially since they follow the same MO that they did in Fallout 2, which means Idea Rehashing. The original Plan was to mutate the FEV into another, entirely deadly strain and release it, killing every other lifeform except those on the Oilrig or otherwise protected from its Effects, i.e. Vaults. Fallout 3 uses the same Idea but in a less overall Function, with the similar Outcome however.
Equally, the Enclave is powerful, the Brotherhood of Steel, at its prime feared the Enclave for good Reason. They had better training, access to much better Technology and Weaponry, as well as Armor. Yet you can easily go toe to toe with a few Squads of them on your own. New Vegas showed just what a small Squad of 4 People and one Vertibird is capable of by comparison against Enemies which are technological inferior, and the Brotherhood is that as well. They are ahead of mostly everyone else, but the Enclave still has the bigger Toys.
That is essentially the big glaring Lore Problems right there. However the biggest Problem with the Game was essentially the forced Story. You get born, grow up and eventually have to leave the Vault and look for your Dad. That is fine of course, but once you find him, why does everyone react to you as if you will help him, or after he dies, carry on his Plans? Whenever did i make that Decision? Why cant i join the Enclave, or any other Faction but am forced to join the Brotherhood? Why does the Game force you to play a good guy? Especially after giving you the Choice to be evil to begin with, which also boils down to a Black and White Morality. Fallout 2 had Morality as well, but it affected the Game in much different Ways.
For example, in Fallout 2 there is a Settlement named Modoc that you run across fairly early on, in the midst of a famine. Now near that Town is a Farm which has plenty of Food, totally unaffected by the dry Weather and lack of Rain. So you are sent to investigate. You have now several Choices.
1: You can just leave and leave the Town to its fate.
2: Go to the Farm and find out who is there.
Thats two clear-cut choices. Lets assume you picked Option 2, you get more Choices.
1: Leave them to their Fate, which essentially boils down to the Inhabitants of Modoc taking over the Farm forcibly and killing everyone there.
2: Make a Deal with the Farmers and the People of Modoc so both Sides can flourish.
3: Kill everyone at the Farm yourself and tell the People in Modoc about it.
4: Kill everyone in Modoc to save the Farm.
5: Do not tell the People of Modoc about what you found at the Farm, essentially lie. Which means Modoc will become a Ghost Town.
There is one good Choice in there, with all other Options being evil, for one side or another.
But alright, lets get one more Example in here. Broken Hills, which you find relatively in the middle of the Game. The Town's main export is Uranium from its Mine. Once you get there and get involved, you have several Options.
1: Just leave again.
2: Help put the Mutant Haters behind Bars.
3: Help the Mutant Haters kill some big Mutants.
Again the whole Questline isnt solved with that however. Lets assume you help the Mutant Haters. It means the town will die because only Mutants are immune to the Radiation in the Mine. Help the Mutants instead? Well, you better fix the Air Cleaner inside the Mine so the Mutants can go back to work. But again it doesnt end there, because even if you do all the good Choices, the Town will eventually vanish because the Uranium will run out, meaning its sole big Export is gone, and with it the Reason of the Town to be there.
So, going over that, Fallout 3 ranks to me like Fallout Tactics does. Its a good Fallout Game, but its not a Sequel to the earlier Installments and as such doesnt really deserve the Number. And yes i got longwinded, anyone being interested in more background Lore, please consult the Fallout Wiki ;P