Continuity mistake: In "Nightmare on Evergreen Terrace", when the teacher hands out the papers before the test, you can see that in the desk sitting next to Bart is a student wearing green sunglasses and has blue hair. In the next shot, Martin is suddenly beside Bart.
Continuity mistake: After Moe yells at Ralph, there's a woman in the background staring at Moe with an angry look on her face. She turns her head away from him after some seconds, but in the very next shot, she is looking at Moe with the same expression on her face.
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)