Mr. Lisa Goes to Washington - S3-E2
Plot hole: The Simpsons take a flight to Washington D.C. for Lisa's speech. But it is revealed in a later episode that Marge has a Fear of Flying. This was before it was discovered that she had a Fear of Flying.
Lisa's Pony - S3-E8
Continuity mistake: When Lisa calls Homer at work, you can see some monitors to his right, and a fire hydrant in back of him. When he turns to his right, you can see that the monitors disappear, the fire hydrant moves, and a green telephone appears next to it.
Continuity mistake: When Homer is writing a note to Marge, he scribbles out Patty's name and writes his own name directly beneath it. When Marge reads it, Homer's name is under Patty's, but slightly to the right. (00:14:30)
Other mistake: When Homer talks to Bart and Lisa through the window, he is standing almost straight up, but considering he is right in front of the TV in the next shot, he would've had to crouch down a little. (00:03:50)
Continuity mistake: When Homer calls the Fatherhood Institute about his poor test results, the guy is holding a cup with 'Super Dad' on it. In the next three shots the cup has jumped to being on his desk. (00:08:50)
Lisa's Pony - S3-E8
Audio problem: When Homer is crying after the tape is finished, what he says doesn't match his mouth. (00:07:25)
Homer Alone - S3-E15
Audio problem: When Marge is running errands, Homer gives her his bowling ball with a bottle cap stuck in a hole. She then takes it to Nicks. When he says, "Sorry lady, you've got the wrong Nicks," he shakes his head and makes an "Ohh" shape with his mouth, not saying anything. (00:03:50)
Radio Bart - S3-E13
Continuity mistake: In the scene where Bart tries to get his radio back from the well, watch the police barriers. When Lou and Eddie get coffee, they walk through one of the barriers, tearing it. Several shots later, this torn piece has vanished, and then the barriers disappear entirely. (00:15:40)
Continuity mistake: When Moe tries the Flaming Homer, there are bottles that keep appearing, and the knife disappears suddenly. (00:06:55)
Continuity mistake: Before the time trials start, the audience on the sidelines keep disappearing and reappearing. (00:12:30 - 00:13:40)
Like Father, Like Klown - S3-E6
Other mistake: At the very end, when Krusty's father throws the pie in his face, the food instantly comes off his face. (00:21:40)
Continuity mistake: When Otto announces about Milhouse's party, 1, Martin is sitting two seats ahead of Bart and Milhouse, even though he was just talking to them, and 2, Sherri and Terri are nowhere to be seen. (00:01:35 - 00:02:35)
Continuity mistake: When Bart realizes he forgot his permission slip, the camera shows us that the paper is half-under his pillow. However, when he got out of his bed at the very beginning, the paper wasn't under his pillow. (00:01:00 - 00:03:05)
Continuity mistake: When Lisa is clapping erasers because she sassed Miss Hoover a second time, the room's clock is visible near the top of the ceiling. However, the clock wasn't there several shots earlier. (00:17:00)
Radio Bart - S3-E13
Continuity mistake: When Rod and Todd talks to 'God' on the radio, the antenna keeps changing position for the entire scene. (00:08:50 - 00:09:40)
Bart's Friend Falls in Love - S3-E23
Continuity mistake: When Samantha is being introduced to the class, there is a boy in The Front row on the right side that is wearing a white shirt and has brown hair. A few shots later (an overhead shot of the classroom), the boy is completely different, with a blue shirt and white hair. (00:04:00)
Radio Bart - S3-E13
Audio problem: Just after Krusty kicks Sideshow Mel into the big birthday cake on his show, he says "Hey kids" but his mouth doesn't move right.
Continuity mistake: When Lisa decides to take Miss Hoover's Teacher's Edition, we see "Teacher's Edition" on the spine of the book. But when Lisa puts it in her bag the spine of the book is completely blank.
Audio problem: When we see Steve Sax driving, he says "What a nice little town" but his lips don't move.
Revealing mistake: When Moe and Barney are seen drinking wine at the wedding, somebody walks away with a tray. When they are drinking the animation is repeated because you can see part of the tray keeps coming on and off-screen. (Look by the bottom right). (00:13:25)