Continuity mistake: In the very beginning scene, where Fry and Leela are talking, there is an explosion. When some ceiling falls down there is one big bit and three small bits next to Leela's foot but then a few seconds later there is one big bit and a few small bits all in different places.
Continuity mistake: Just as Hermes A is about to shoot the box into the sun, all the crew (A and B) shoot out into the airlock. However, Hermes B doesn't come out of the box and just appears in the pile. This is confirmed in the commentary.