When Apu comes onto the mountain, his skin is yellow.
When Bart pulls the string on Skinner's weather balloon, it's not visible in his hand in the previous shot of Bart.
When Professor Fink is about to show what the town needs to do to stop the comet from hitting Springfield, we see two people behind the display table. They disappear in the next shots.
Selma says that "a lady goat is called a sheep." This is incorrect, goats and sheep are different animals.
Bart is seen writing with his right hand while standing. He is well-known for being left-handed. This is corrected to writing with his left-handed in the next scene when he is laying down.