Deliberate mistake: In "Dial Z For Zombies", Homer is shooting zombies with the shotgun at the school. When he shoots the first two he just shoots them twice. Every other zombie he shoots requires him to slide the gun. It doesn't when he shoots the first couple of zombies.
Continuity mistake: When Marge comes to pay for her shopping, she empties her left pocket on her coat, but when Sanjay finds it in her pocket, it's in her left pocket. We know it wasn't in her pocket anyway because when Sanjay finds it, it is bigger than the size of her pocket.
Continuity mistake: When Homer is eating the bacon and what looks like scrambled eggs after claiming Marge's oatmeal had a bug on it, the close up of the bacon shows that it is pink/purple and the eggs are yellow but the in the following shot, when Bart says, "Dad, there's a bug on that." the bacon and the eggs switch colours.
Continuity mistake: You may have to look carefully for this mistake. When Marge picks up the 'Das Butt' video, you can see the cover. In the next shot, you can see Marge holding it so you can't see the cover. But when she hands it over to Ruth, she twists the video round and you can see that nothing is visible. You may have to see it a couple of times.
Continuity mistake: When Homer is in Lisa's classroom and imitates a farting sound, there is a sink at the back of the classroom and nobody is using it. However in the wide shot, there are suddenly two people by the sink. When the shot is back to Homer, nobody is by it. (00:03:00)
Continuity mistake: When Bart arrives at school in the bus, after Homer plowed the road for the bus, the sidewalk is covered in snow except for Martin's footprints. Then, when he gets out, the sidewalk has been shovelled, as there is no snow on it. Following this, Bart is pelted by snowballs, which sends him falling face-first into the sidewalk, which is once again covered in snow. (00:10:20)