Polly Wants a Treasure - S1-E8
Continuity mistake: In the scene where Baloo and Kit walk through the Sea Duck's cargo area to try and find who they think is a stowaway, Baloo lifts a crate of fragile crystal glasses over his head. The crate rotates between shots, judging by its red "Fragile" stamp.
Other mistake: In one shot after the droid fight in Gha Nachkt's ship, at one point when you see R3-S6 (Goldie), his eye is reversed. (00:12:42)
Heart of Archness: Part III - S3-E3
Continuity mistake: On the way to the helicopter, Archer stops the group to ask about the lacrosse game. Archer has the pirate held at gun point and the two are standing mere inches from each other, but when Archer says to Lana she is his only friend, the pirate is nowhere in sight.
Safety First/Crime Sheen Investigation - S1-E12
Other mistake: During Crime Scene Investigation, Jimmy explains his costume to Carl and, while saying "Sherlock Holmes", his chin goes into his jacket. (00:14:38)