At the end of "The Cryonic Woman" Fry is ditched froma moving spaceship, and told that he can never have his job back. How, then, does he come to be alive and well, and a Delivery Boy for PX in the very next episode???
This is one of 3 big continuity errors which I feel greatly conflicted over. The second is in "When Aliens Attack" and the whole of NNY is destroyed at the end of the episode but by the start of the next episode everything is back to normal. This is probably the most forgivable of the three as it is, as someone mentioned earlier, just property damage, and could've been sorted out by the start of the next episode. I still think I might've preferred the episode without this joke though as it kind of contradicts itself as it is trying to be "clever" by joking that it's broken one of the rules of sitcoms, but it overrules itself by pressing the reset button ready for the next episode.
The second of these is at the end of War is the H-Word, when Bender correctly guesses the trigger word (antiquing) and sets off a bomb designed to wipe out all life on a planet inside the Planet Express HQ. Yes, it was a fairly funny joke, but it is another one of those things that clearly can't be canon, which annoys me slightly, as canon is one thing that Futurama does in a better way than most cartoon series. I think that this part is at least as unforgivable as the Cryonic Woman scene. I would be interested on hearing your view on the WitHW scene Tnuk.
I think overall though, I have to just tell myself that it's a cartoon and it's allowed to use "Cartoon Physics" from time to time.