Continuity mistake: When the Detectives are talking to the Chief about the Blues the Chief is peeling an orange: which gets peeled, the skin is thrown down on the desk, then it gets peeled again until the detectives leave the room when the orange peel hits the desk again.
Other mistake: In the scene after Jeff 'singlehandedly foils a bank robbery' and is arrested, Mrs. Blue and baby are sitting at the detective's desk. In the background of certain shots you can see Sawyer on the phone, always in the same position. But a moment later, the phone rings, camera still with Sawyer still in position although he doesn't move to answer the phone or speak. Then he moves and announces to the detective that the phone is for him when he didn't even answer the phone.