Phixius

Corrected entry: The treehouse tree, in reality would not go up and down when the rope goes back and forth, but would collapse anyway.

Correction: It is a visual gag in a cartoon and is not expected to reflect realism.

Phixius

Corrected entry: Frink couldn't have perfected his acid drill without being outside the dome where it also is.

Correction: Another possibility is that he just perfected his acid drill but was separated from it by the dome.

Correction: It's a gag, not a "deliberate mistake". No different than Homer's hair coming out like an unraveling thread, or the fact that it supported Bart's weight, or the fact that Homer and Bart were able to drive around on the dome like they did.

Phixius

Actually, he was separated from his drill by the dome.

Corrected entry: While on the cycle Bart pulls some of Homers hair of but after the bomb explodes his hair is back to its usual status.

Correction: It's a visual gag of such commonplace stature that this can hardly be considered a continuity error, especially in a cartoon.

Phixius

Corrected entry: When the Simpson family are at the motel after getting out of the dome, Homer knocks on the door to ask what the secret knock is. The door opens without Homer opening it, and the rest of the family is nowhere within arm's length of the door to open it.

Correction: One of them strode forward, turned the knob, then, as the door was swinging open, strode back to wherever they were so they wouldn't have to greet or otherwise acknowledge him. Every hotel/motel I have stayed in had doors that swung open if the latch wasn't in place; it's so you're less likely to lock yourself out.

Phixius