Continuity mistake: When Fry, Leela and Bender enter the orphanarium you can see 3 owls. In the next shot you can see 1 owl walk down the corridor. In this shot you can also see the door and no owls go through there, but in the next shot the other 2 have disappeared.
Continuity mistake: In the scene where Leela and the doctor are driving out of town and throughout the episode Leela's second eye is following her motion. This despite the fact that in a previous scene we could see that she was unable to move her second eye. (00:09:55 - 00:12:00)