Continuity mistake: When Wallace is put into his overalls he's still wearing his green pullover. A moment later he suddenly doesn't wear it anymore but a complete white shirt. He couldn't have just taken off the pullover as the shirt under it is actually fake (The collar is actually part of the pullover and the arms are just stuck on).
Continuity mistake: When Wallace and Gromit are being chased by Preston in the sheep truck and Gromit grabs the window cleaning ladder, he puts it up in the sidecar before climbing it and having the bike do a 360 degree turn. But after the turn is complete and he climbs back down (the bike is still in motion at this point), the ladder has magically moved onto the motorbike.