Revealing mistake: When the policemen are looking for Jack who poses as a hobo, and when Lopez confronts him and gets killed, the scene is supposed to happen to during the night, but what appears to be daylight comes through the openings (we see the outside of the building when they all escape and there's no light source like that). (00:53:15)
Continuity mistake: When "Highball" scores a strike against the hobo, there is a reaction shot on the 4 homeless guys to the right. The one closest to the camera (rightmost one) is watching with his right hand on his knee, but his hand is on the hat he's wearing in the next shot. (00:58:10)
Continuity mistake: During the stunt where the motorcycle goes down the flight of stairs, the actors are replaced by stuntmen - and the one replacing Biff Manard wears the jacket buttoned up all the way, as opposed to the actor. (01:02:10)
Other mistake: Jack realises that he 'lost' the watch, but luckily Leena shows she wasn't as forgetful and it's in her possession. We saw Jack toss the watch as ordered by the possessed policeman. We saw also Leena show up to save Jack, and leave the scene with him hand in hand - he dragged her with her, actually. She was nowhere near the point where the watch would end up, and she didn't have a chance to get it later, especially without Jack's knowledge.
Other mistake: The policemen work with Whistler all day long doing his bidding, to the point of shooting an unarmed woman, but they show the big-lipped zombie Trancer look only at the very end, in contrast with everyone else who would fully transform into a Trancer the moment they commit to attempting to kill someone.
Plot hole: Whistler's powers are not fully explained, but most certainly he has no god-like abilities or is omniscient; the rest of the movie shows he is not. But Jack's first run-in with a Trancer in 1985 LA makes no sense then; unless Whistler was mentally controlling every mall Santa in LA, he had no way to know where "Philip" would end up. If he did (and again, how could he; he doesn't have the power to control legions of Trancers), he would have capitalized on it catching him in the act with the police, too.
Other mistake: The watch that the poor man's Q of this movie provided is supposed to buy 10 seconds of time ("1 second stretched to 10, single use", that activates when he presses the wheel), but the power works in a completely different way, since in those "10 seconds" Deth takes his time to assess the situation and watch bullets float, then grabs Helen Hunt, stare his mortal enemy down without doing a thing to him and then carries her from the back parking lot of the store to the car parked in the front. Not even Husain Bolt (at most Dio Brando, with a very similar time-freeze gimmick) would be able to do that, not to mention that flying bullets somehow are slower than liquor pouring from a bottle.