Continuity mistake: In this episode, Mr Burns and Smithers are on the balcony of Burns' office. Mr Burns says "It will be like taking candy from a baby. Hey, that sounds like a laugh. Let's try it right now." We see Smithers, whose expression doesn't change as the two go back into Burn's office. In 'Who Shot Mr Burns Part 2', Smithers remembers this event, except now he looks quite shocked when Burns mentions about taking the candy.
Continuity mistake: Right at the end Lisa is holding a doll head and some cards. There is a very brief shot of Bart, and then when it's back on Lisa she doesn't have anything in her hands when they hug. There wasn't time for them to be put down and you cannot see them anywhere either.David Mercier
Continuity mistake: In one of the shots after Mr Burns has broken the fortune cookie, the remains of it vanish from the table. There is something else on the table, nearer Smithers, but it and the cookie are very different shapes, so it's very difficult to confuse the two.David Mercier
Continuity mistake: At the fair, Helen Lovejoy picks up a pita and bites a corner off it. There are a few angle changes and when it goes back to her and you can see her pita looks untouched. It's unlikely she just picked up another one or finished a whole one in that time.David Mercier
Continuity mistake: At the birthday party Maggie is playing in the sandbox with one of Apu's kids. She and Apu's son both have pink with green polka-dots party hats on. After she is taken out of the sandbox by Moe, Homer takes her and she keeps squirming out of his arms. Look on her head and you'll see that her party hat has disappeared, and never comes back.