Frank's prison tattoos change position throughout the movie.
After the chase scene near the end of the film between Joe in the police car and Frank in the Buick, Joe turns off the red police lights, then the car's headlamps and steps out of the car and stands next to it. In the final scene we see Joe still standing next to the police car but the car's headlamps have mysteriously come on again.
At about 40min when Joe and Maria have Mr. Roberts over for dinner the baby grabs and starts eating a piece of bread. As the scenes change the amount of bread eaten decreases and increases.
When Joe confronts Frank in the bar, Frank has a freshly lit cigarette in his mouth. When the camera angle changes he's lighting a match to light the same cigarette.
At about 1hr 30min when Joe comes to rescue Frank from his bar fight Joe gives Frank a cigarette. In the first scene the cigarette is in the right corner of his mouth. When we see Frank from a difference angle the cigarette is in the left side of his mouth.
During the "mirror" scene, the "from behind" shot and the "mirror" shot don't match. (This actually makes sense, given that the camera would have been visible from the angle the scene is presented.)
When he takes the shotgun out of the patrol car, he racks the action and a shotgun shell flies out and can be seen in mid air. If the shotgun was already loaded, there was no need to rack the action as there was already a round in the chamber. In real life, he should have known there was a round in the chamber because he would have put it there before going on his shift. In real life, ejecting a round would be because of stress in a shooting situation.