Deliberate mistake: When Dory is inside the whale, she doesn't have the scars from the jellyfish sting anymore. [This is actually a long-standing Disney tradition. The company seems to believe that it is less traumatic to see violence onscreen if the evidence is gone immediately (blood, scars, etc. always disappear). Still an error, but it wasn't the fault of the CGI animators.]
Factual error: At the end of the movie it shows all of the aquarium fish in the ocean inside of their bags. It also shows the bags almost completely out of the water with only a small portion under water while the bags are almost completely filled with water. With this amount of water the bags should be submerged underwater with only the little amount of air showing on the surface, because water is not lighter than water; water weighs the same.