'Otoko rashiku' de ikô! - S1-E1
Continuity mistake: During the episode, whenever the crew watches Akito fight, the shots from behind show to the right of the nasty admiral Sadaaki Munetake (the guy with the bad bowl cut) his fellow with blue hair, and to his left the short guy with a moustache. In the front views, it's the opposite. The Prospector (the brightly colored fellow, purple pants, pink vest, yellow shirt) also appears in the front view but is nowhere in sight in the back shots.
Midori no chikyû wa makasetoke - S1-E2
Other mistake: When Yurika restarts the Nadesico, one of the screens pop up with a huge congratulatory "SAFATY ROCK OFF." (00:18:05)