Continuity mistake: When Martin meets his parents in their house, the door is split and closes in the middle with a screen. In the next shot, it is a full door without a screen.
Suggested correction: As seen from the exterior, the outer door is a very wide screen door with its handle to the left and hinges at the right. Behind the screen door are two solid doors which swing open inward from the center. Notice the wide screen door is the door Martin bangs on when his father closes the solid double doors (with individual doorknobs), and later in the episode when Martin's mother walks outside we see her push open the screen door.
Other mistake: When Ferris first arrives in the town the the church bell chimes seven times indicating it's 7 o'clock. Later the bells chime again but this time only four times indicating 4 o'clock. Surely he didn't walk around the empty town for 9 hours.
Suggested correction: Since the revelation of the episode is that Ferris is merely in a simulation, it stands to reason that they control how quickly time passes for him.
Plot hole: If Walter was indeed immortal from his deal with the devil then there was no reason for him to use the Escape Clause when he was sent to jail. Since he can't be killed by any means and nobody can harm him there would have been nothing to stop him from escaping the prison the moment his cell was opened.
Suggested correction: He may be immortal and not feel pain, but he isn't super-strong and can't walk through walls or people, so escaping wouldn't be trivial. That isn't to say it'd be impossible or even that hard, but this is a man who got centuries of perfect youth and health, and all he could think of to do were things that would kill a normal human (even though, again, he can't even feel pain.) He also confessed to murder to experience the electric chair, not considering that they wouldn't just let him walk away when he survived execution. He's a short-sighted, unimaginative moron, and that's probably why the devil chose him.
Suggested correction: Walter uses his Escape Clause because he doesn't want to live forever in a prison cell. Even if he could escape at some point, he's not willing to spend any time behind bars waiting.
Factual error: Caswell acts surprised at the sight of the lighter, but lighters were around in his time.
Suggested correction: The modern lighter, which use ferrocerium to create a spark, was developed in 1903. Caswell was from 1880. This would have been different then anything he would have seen.
Other mistake: Bemis is happy because he has enough time to read all he wants, but all the food would be poisoned by the radiation and and even if it wasn't, meat and fish it would spoil from not being refrigerated.