When Miles first enters police station there is a red hair in ponytail man with a beard in cuffs entering the scene with arresting officer holding him.
This exact same shot, with same actor wearing same outfit is seen later in the film with same arresting officer.
It's not used as a gag- it's laziness, as they just used same shot twice.
When Miles first enters the department as a detective, Detective Larson is shown loosening the handcuffs on a suspect. The shot shows that only one handcuff is released, but yet when the suspect runs, there are no handcuffs on him at all, when there should be both hanging from one wrist.
When Miles is hanging in mid-air in the opening chase, he pulls out a circular saw to cut through the rope he is hanging from. He cuts the rope in front of him which would have made him fall backwards, but he falls forwards instead.
When Miles is talking to his girlfriend after coming out of jail, there is a person on a bike visible in the background. The person is in a riding position, but the bike is not moving. If you look closely, you can see that person is leaning on his left leg.
When Miles is dressed as a pizza delivery man, he opens the front door of the police station and a wall holding a bulletin board is visible just in the door. Though when showing a shot of the interior after he walks in, the room is an open space with no dividing walls in front of the doors.