Continuity mistake: When Maggie (sitting on Marge) appears on "Tyrano-Vision," Homer waves his hand in front of her. However, we can see that he isn't leaning over too far, and in the next shot it is clear that both Bart and Lisa are sitting between Homer and Marge, so there is no way he could have reached over to her in the first place.
Continuity mistake: When Burns first shows the team the nerve tonic, the "&" on the 'Brain & Nerve Tonic' label is facing backward, but as Burns pulls it away it faces forward. Then as he moves it around as he's talking, the "&" switches between facing forward and facing backward again. This happens all in the one shot.