American Dad (2005)

The Worst Stan - S7-E4

Continuity mistake: Stan's crocodile skin tie changes back to his ordinary black tie when he says "Prison rules" to himself.

Nikolai

The Kidney Stays in the Picture - S7-E16

Plot hole: It is explicitly stated in this episode that Hayley was conceived in 1996. While normal for shows without character aging to change birth years to benefit the plot, this move was premature. Hayley's permanent age is stated as 18, and this episode implies that in 2012 she would be much younger than this. The whole plot centres around her being legally able to drink in a bar, so this is a pretty big mistake.

Food Blog

The Scarlet Getter - S7-E6

Continuity mistake: The poop on the edges of Roger's robe that Stan wears disappears in later shots.

Casual Person

Stanny Tendergrass - S7-E9

Continuity mistake: We see an old lady shoot a yellow arrow at Roger's golf bag. The shot changes and when we see the arrow again it is red. (00:09:35)