Continuity mistake: In the intro, before the main titles, the Professor informs the crew that he's booked them on the maiden voyage of the Titanic. When Leela says "Looks nice," at the beginning of the "scary" Titanic montage, the right side of her shirt is undamaged. During the middle of the "scary" Titanic montage, it suddenly becomes torn.
Continuity mistake: During the Titanic's naming ceremony, Zapp stands next to the ship, with the word "Titanic" in shot, just above the grey part of the hull, very low down on the ship. However, during the rest of the episode, the word "Titanic" is located further up, just below the white trim.
Other mistake: Bender wears a magnetic bow tie. However in series 1 episode 2 it's shown magnets screw up his circuits and make him sing songs. It's mentioned in a previous entries correction that it's only when the magnet is near his head. This isn't true as it's shown in others episodes that it happens when a magnet is attached anywhere on him.