Plot hole: When Andromeda and Perseus wake up on the beach, Andromeda tells Perseus that Argos needs a new leader/king. The problem with this is there is nothing onscreen to show that she even knew her father the King had died. She was hanging by her arms facing the Kraken and she couldn't turn around. By the time her father died, she was already falling into the sea, so again, she shouldn't even know her father has died.
Continuity mistake: Towards the end of the film, there is a shot of Andromeda being led to be sacrificed, in this shot you can see that she is wearing sandals that are laced up her legs, and have no way of falling off. However her sandals are gone when she's under water, before Perseus dives down to rescue her. Lying unconscious on the beach, she has bare feet.
Continuity mistake: Right after Perseus kills the former king (he stabbed Io in the back), he gets up to his Pegasus, rushes back for his sword and Medusa's head. In the shot of him going for the Pegasus after he picks the head up, he is seen without it for a shot. He immediately has it in the next.