The whole FEV thing on the East Coast in a Vault. The whole thing makes little sense.
As for the Enclave and Brotherhood, there was an explanation, weak one but it was given.
I am kinda ticked about Harold, but that isn't really inconstant.
The only real big inconstantency that isn't really explained is the setting of Fallout 3. Radiation still being around after 200 years. No real progress at all in that time. No healthy living green plants or trees anywhere but for Oasis and later Point Lookout. That and its the capital of the United States yet it looks in very good shape, having gone through a nuclear war and 200 years of neglect.
Edit: I try not to think about it, so that's why I didn't include it. Mothership Zeta is the DLC equivalent of the Burned Game.
...thats it? Surely there is more? Some ppl seemed so irritated about it. Guess that is the interwebz for ya...
It isn't so much the inconsistancy as in crapping on canon of the past games that is the problem. Its the piss poor writing throughout the game and the numerous plot holes in the game. What little Bethesda did try to explain, was have half assed and not a very good explination at all.