Continuity mistake: When all the people who are plotting to murder Homer are talking about the reviews Homer had given them, Akira says, "So why did you put yours in the window?" and you see the review. At the end of that scene, when they are all laughing, you see the building they are in, and it has nothing in the window.
Revealing mistake: When Homer is giving Marge, Lisa and Bart money, Homer puts his hand on Bart's shoulder and whispers 'Mel's movie really stinks'. When he lets go of Bart to say this, he leaves his fingers on Bart's shoulder, but he still has fingers on his hand.
Other mistake: When the Simpsons' drives the electaurus off the edge of the harbour, it is shown that the front of the car goes downwards. When it cuts to the interior view with the Simpsons' screaming, the view from the back window is tilting down, suggesting the rear is going down and the front coming up. But in the next shot the car is seen in the water with the front down.
Continuity mistake: In "Desperately Xeeking Xena", as Lucy Lawless grabs the lips of the Collector, you can see a big "C" on the back of his cape. After she has thrown him across the room and he gets up, the "C" is gone. It reappears later in the fight.
Continuity mistake: The "dummy" in the episode changes consistently from a real character to a dummy sometimes. When Mel jumps into the vehicle in the museum the "dummy" moves aside. When Mel shoves it out of the way, it stays in one rigid position as if it is a dummy. During the chase, the "dummy" falls on the car behind and its facial expression changes. But when one of the guys from THAT car (not the one Mel was in) goes to the dummy, its head is ripped off and you can see that it is stuffed.
Other mistake: In "Desperately Xeeking Xena", at one point she approaches the Collector, who is about to get a light saber. We can see the back of the pouch that Xena is in, but the tape on the other side isn't visible, even though it is a transparent pouch.
Continuity mistake: When Lisa is on the television talking about her tax rise, we see inside Moe's tavern. Look at where Lenny and Carl are sitting because they have moved 3 or 4 seats down when we go back to them later on. And there is no reason why they would they move like that.
Add timeDavid Mercier
Continuity mistake: This mistake happens twice in the episode. At first, when Homer arrives on the island, he gives the islanders some bibles and says "Knock yourself out." Ack says that they cannot read. Yet later when Homer is revealing the casino, Ack reads "The Lucky Savage-?"
Continuity mistake: At the beginning of the show, the hospital Mr. Burns is at has a sign in front of it that reads, "Got Tumor?", but when we see the hospital again it isn't there. Additionally, the "Mayo Clinic" sign atop the building gets noticeably smaller in the second shot.
Continuity mistake: When Moe is going to get a plastic surgery, the surgeon draws some marks on his face. You see Moe from a side view, and the marks on his face aren't visible from that angle. However, the marks on his face suddenly appear and you can now see them from that angle.
Continuity mistake: In "I Know What You Diddly-Iddly Did", there are a few errors: Homer says, "Guess I forgot to put the fog lights in" at a slightly higher pitch to when we heard him say it earlier (When the event actually happened). When Marge actually ran over Ned she did not carry on driving. The flashback shows that Ned was run over without glasses. However in the actual event he had glasses on.
Continuity mistake: When the Ranger stops the Simpsons' car at the start of the episode, watch his "class ring". When he puts his hands inside the car it's on the left hand. However, the flies later eat his hand and take his ring, and it's suddenly his right hand they ate and took it from.
Add timeDavid Mercier
Plot hole: In "Life's a Glitch", Lisa finds out that she has a seat on the spacecraft going to Mars as the proofreader. How, though, was she not informed of this before going to the rocket? The family only finds out about the rocket after finding Krusty's letter/invitation and the fact that she was on the list there would be no reason why she wouldn't have been informed of this. It was still New Year's Day so if it had been by mail then it would have to arrive before the New Year so as to make the plan work, being as it was a public holiday and no mail would be delivered. Therefore it would have to be delivered personally or someone would need to contact her. There were also many well known celebrities and figures ready to board the rocket. I can't imagine they were all home in time to gather their mail and were all somehow contacted, yet Lisa was simply walking around town and at church and they couldn't find her? There was also no evidence to suggest anything would have stopped her from either receiving the invitation in time or being informed of the mission.
Revealing mistake: After Lisa says "For a product that's evil and deadly" while standing in front of the tomacco stand, there's a duplicate Lisa behind her that stands still while she moves, giving Lisa the appearance of having two heads. It looks like the animators made a mistake while trying to animate Lisa.