Continuity mistake: When the robot at the start is dying, the doctor opens a panel to see his "heart beat." After a couple of other shots we see the panel again and this time it's closed without anyone touching it. It's also important not to confuse the doctor closing the robots eyes with this panel. (00:00:35)
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.