In the scene where Wayne is investigating the domestic dispute across the hall, the cop is wearing no top or pants, yet he pulls a badge from his person.
In the initial scene when the driver is shot in the head, in order for his blood to have splattered on the window in the manner that it did, the bullet would have had to pass through his head and then through the window.
The blood under Frank's (Bill Murray's) nose after the fight at the end of the movie doesn't change at all for a while, then when in the Cadillac it does.
In the scene at the police station where Wayne is typing up a report while he talks to Frank, he uses white-out to correct a mistake. But since he's using a multi-part form, the typo would only be fixed on the top copy.
Wayne wears his class ring on his left hand, instead of his right hand which is the tradition.