Other mistake: At the end, when Fry, Leela and Bender are sitting at the table, Fry's legs disappear (and the gray blotch beneath him isn't them - it's the table leg; and it's not hiding them either - his knees should be visible behind it).
Continuity mistake: As Bender goes up to the Oilade stand there are four full glasses on the table and a large jar next to them. Bender drinks one of the glasses of oil and puts it down. He picks up another glass leaving two full glasses and one empty one on the table. The following shot there are now three full glasses. After this there are still three full glasses but the glasses have moved to the other side of the stand. The next shot the jar of oil disappears.