Continuity mistake: Treat Williams is drinking a brown liquid from a glass (scotch?) while accusing Gina Carano of having something to do with his son's disappearance. Shortly afterwards, the liquid is a different color and the glass is much more full. (00:41:40 - 00:42:40)
Plot hole: Lamar was a star basketball player who didn't pay attention in Jim's English Literature class (and wasn't "good in English") but needed to pass to continue playing. Lamar told Jim, "I've had four courses with you" and "I'm a Junior." Whether this was Lamar's 4th or 5th English course, neither make sense. A fourth course would equal 12 credits - enough to be Lamar's' declared major (unlikely) - and most students don't enroll in the same professor's courses when they don't do well ("easy A"). (00:43:56 - 00:46:40)
Character mistake: When Jesperson imagines himself as a Mountie his uniform is completely wrong and is not even the right colour. As it was his ambition to join the force and he has photos of RCMP officers in his cab, it seems unlikely that he would imagine himself in a completely incorrect uniform.
Suggested correction: It's not a character mistake, for the reasons stated; it's a clear factual error from the filmmakers.
It's a character mistake since it's his imagination and, as you stated, it's not something the character would get wrong.
Revealing mistake: JR is in the weapon container of the crazy dealer, who passes him some of his goods. JR ends up holding in his right arm a MP5K and an M4A1, which combined are about 5 kilos, but then he passes him an M60 Machine Gun, which weighs over 10 kilos and that the relatively diminutive protagonist just handles throughout the scene gripping it with his left hand and making no effort whatsoever. (00:25:20)
Continuity mistake: When Nick is instructed to leave hotel room #700 Chord verbally tells him to "go outside and turn right." but the on-screen arrow points left and we see Nick turn left. (00:29:39)