Funeral at Fifty-Mile - S1-E22
Continuity mistake: When Jessica walks from the house to the barn at the end, she is wearing knee high brown boots. By the time she reaches the barn they have been replaced with court shoes.
Revealing mistake: When the thief places The Blue Carbuncle in the goose's throat, it's obvious he actually doesn't put the gem in the bird's mouth. He pretends to, but then drops the gem into his other hand. This is all visible in the shot.
The Hottest Guy in Town - S1-E2
Continuity mistake: It's stated in the pilot episode that Syndey married Raymond first. Yet in episode two it's said Carole married him first.