Continuity mistake: Close to the end when Edward Norton runs up to the front of the empty building and Brad Pitt appears, he tries to break the glass door by pushing a bench into the door, but it doesn't work. He doesn't move the bench and he then shoots at the glass and breaks it. When it shows him walking through the broken door, the bench has disappeared.
Continuity mistake: When the Narrator and Bob are crying together at the support group, Bob is much taller than the Narrator. However, when the two meet in front of Marla's place and Bob tells the Narrator that he is a member of Fight Club, the Narrator is taller than Bob. Edward Norton mentions this on the commentary. He is actually taller than Meat Loaf, but Bob is supposed to be taller than the Narrator. It seems they didn't remember to make him taller in every scene though.
Continuity mistake: In the scene towards the end where The Narrator is trying to break into the building, he smashes the bench into the door and fails to break the glass. He then shoots the glass with the pistol and it jams. The camera cuts to the next shot and the pistol is no longer jammed.
Continuity mistake: In the scene in the bar right after Edward Norton's apartment blows up, watch the men playing pool behind him. Towards the end of his conversation with Pitt, there is a continuity error. One of the men is bent over getting ready to take a shot. A mere second later, he's on the other side of the table and his opponent is finishing his own shot.
Continuity mistake: Near the end of the movie in the underground car park, Brad Pitt pushes Edward Norton into the wingmirror of a van. The mirror flips back against the van and stays there. A couple of shots later we see Brad Pitt check his face in the mirror, which is at a different angle to what it was before.
Continuity mistake: When they are preparing to confront the City Councilman, Brad Pitt's character pulls him in to the bathroom. If you really look at the locks on the door you see that as he is pulling him in there is no deadbolt lock, but when the Councilman is halfway in through the mirror you can see that the same door has a deadbolt lock.
Continuity mistake: When Tyler Durden goes to Marla's apartment to prevent her suicide, he removes a cigarette from his mouth and gestures as if he is throwing it down on the floor at the top of the stairs. Then the cigarette is back in his mouth when he proceeds to the door, at which point he really does throw it down on the floor.