Revealing mistake: When he old lady jumps over the counter to attack Jack with a cleaver, she is replaced for the physical struggle by a younger person; you can see her face when the two struggle against the table. (00:04:55)
Character mistake: In the opening credits, the actor Art LaFleur, correctly credited as such in the end credits, appears as "Art Le Fleur" (00:01:00 - 01:15:50)
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.
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.
Plot hole: The 'medics' carry the body bag that is supposed to have the body of Evil Santa inside, but Whistler vaporized it. Somehow, they fail to notice that the obese man weighs like a feather and the bag is deflated and empty. Moreover, the other Trancers vaporize within seconds from their death, but that one, and only that one, took minutes or even hours to disappear, only with Whistler's direct intervention. (00:25:00)
Other mistake: Jack receives a summons from the officers, but he wants to ignore it. He's arguing with his former colleague on the beach. His hair is wet but the suit is dry. (00:08:30)
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.