Continuity mistake: When Homer remembers finding out that Marge was pregnant with Bart, he screams, tears out his hair and runs upstairs, past a picture of Lisa in the pink hat she wears to church. This mistake re-occurs seconds later when Homer remembers finding out Marge was pregnant with Lisa. Hard to have photos of Lisa on the wall before Bart and Lisa were even born...
Continuity mistake: In "Time and Punishment", when Homer returns to the basement after his first time travel, there is a scorch mark on the work bench where the toaster was placed when he turned it on. The angle changes to a shot from the stairs, and the scorch mark is gone. Later in the episode, the mark is back on the bench.
Continuity mistake: Bart comments on Homer's extreme reaction when he realised Marge was pregnant with Maggie. In the next flashbacks, when Homer reacts in the same way to hearing about Bart and Lisa, they are shown in the house at Evergreen Terrace both times. In Series 4, in the episode Lisa's First Word, they show that the Simpsons did not move to Evergreen Terrace until just before Lisa was born. Other episodes have also shown that Homer was with Marge at Doctor Hibbert's when she found out about her other pregnancies.
Continuity mistake: Homer's two hairs over his head are dishevelled when the family arrive at Itchy and Scratchy land due to whatever has happened on the detour - however, it suddenly changes to being like he normally has it in the last frame that shows the family in the car, before the car park is shown.
Plot hole: When Homer is seen at work in the flashbacks (before Maggie was born), he is at his usual control panel in sector 7-G, but he only began working here when Burns made him safety supervisor in season 1, "Homer's Odyssey". Before Maggie was born he should have been working at the conveyor belt with the carbon rods, where we saw him in the first couple of episodes.
Continuity mistake: When Homer's badly-edited "Rock Bottom" interview is shown on TV, the hands on the clock behind him keep jumping around between all the different cuts. But when we saw him giving the actual interview earlier, the clock behind him stayed at 5 o'clock the whole time. The hands on the clock are also slightly different.
Continuity mistake: When the Simpsons are eating and the family are praising Marge, Homer's plate is first seen to have a small amount of yellow food and a bit of pink food (meat?).In a later shot when Homer steals and uses Marge's pepper spray he has a large pile of yellow food.