Factual error: When Chief Wiggum opens the revolver's chamber, there's 5 rounds with one open slot. In the next shot, we see the reverse end of the chamber and it's drawn in such a way to indicate those 5 rounds all have bullets in them still, meaning the empty slot is from when Maggie shot Mr. Burns. But revolvers don't eject spent shells automatically and no one handled the gun after it dropped on the floor. So the empty casing should have still been in there when Wiggum opens it up for the first time.
Continuity mistake: As Chief Wiggum is being interviewed about the fugitive, his arm is shown to be in a cast due to the police van crashing at the Krusty Burger Drive-Thru earlier on. Yet when they get to the hospital, his arm is completely fine. (00:17:30 - 00:19:00)