Continuity mistake: In the sequence with the boat, its position changes. When Nemo is looking at it with his friends, it is a long way away. When Nemo gets angry and swims to it, it's suddenly very near the reef. Then, the diver catches him when he's only been swimming away from the boat a few seconds, but the diver has to swim a long way back to the boat. Finally, when Marlin follows the boat, it's very near again, because he gets there before it starts, even though he was temporarily blinded by the camera. The boat does all this without raising the anchor until it leaves.
Continuity mistake: Towards the middle of the movie, we see a shot with Nemo staring out of the tank, depressed. The camera slowly pans toward the side of the tank and Nemo is reflected in the glass twice. However, towards the end of the movie when Nemo is playing dead, all the fish swim to the other side of the tank and Bloat says something like, "What's happening? Why is he playing dead?" The camera pans to the side of the tank again, but the fish are only reflected once this time. They should have been reflected twice.
Continuity mistake: After Dory and Marlin passed the jellyfish and Marlin passes out, when the movie returns to the tank, the camera pans over the tank from right to left, and there's a reflection of the Sydney skyline. However, neither walls nor window frames show in this reflection.