Whenever Dory & Marlin race in the jellyfishes, Marlin wins but has to go back and look for Dory because she was lost. She apparently got stung, and so during the movie she has a scar right by her right fin. At the end of the movie, though, she waves to Nemo as he goes to school. She suddenly has no scar there!
This is not a slip-up. Yes, getting stung by a jelly fish would leave a scar on a fish, but not necessarily one that would show so obviously forever. When Dory waves goodbye to Nemo at the end, it is much later and by this point, chances are, the scar would be barely noticible, if not gone completely.
As you will notice with all Disney films any character who gets a scar or cut/blood they only stay for a short while, this is so not to upset the children,