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.
Revealing mistake: Before the final fight scene between Tyler and the narrator, Edward Norton points a gun at Tyler telling him to step away from the van. Tyler breaks the key and throws it away. When this shot is seen through the security footage, then in the far left security computer screen we can see that there is already a gun shot hole in the back window of the van, and there is also some random guy walking in the top left corner of the screen.
Revealing mistake: When members of Fight Club are starting fights, watch VERY closely when the guy with the hose sprays the vicar - you can see the camera wobble slightly (looking on the left of the screen at the top of the fence is a good reference point). This happened because the cameraman started to laugh.
Continuity mistake: When the narrator first meets Bob, Bob starts telling him how he used steroids. In one shot we see the narrator's right hand is resting at the middle of Bob's back, but in the next shot we see his right hand at the top of Bob's back and a little above his armpit.
Continuity mistake: Check out the sweat stain around the collar of Ed Norton's t-shirt in the scene towards the end of the film where he is being interrogated by police. It keeps getting bigger and smaller from shot to shot.
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: When Ed Norton is blackmailing his boss the thermostat changes from white to black in some of the shots. The chair moves a bit to the left too.
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.