The 'trench' encountered by Marlin and Dory is actually an undersea canyon, since it rises above the ocean bottom. Trenches are miles-deep depressions in the sea floor, like the one where they found the diver's mask.
When Mr. Ray sings his "Let's Name the Species" song, he isn't actually naming species. Porifera, Coelenterata, Ctenophora, Bryozoa, Arthropoda, Echinodermata, and Chordata are all phyla. Hydrozoa, Scyphozoa, and Anthozoa are classes in the phylum Cnidaria (Coelenterata), and Gastropoda is a class in the phylum Mollusca. The order of classification is: kingdom, phylum, class, order, family, genus, species. Phyla and classes are definitely not the same as species, although it is revealed, in the DVD, that Mr. Ray isn't an actual scientist, more that he just picks things up. In that case, it could very well be that he mistook the one for the other, not knowing that he was passing on incorrect information.
The instrument that is used by the dentist that is mentioned in the movie is called a "gates glidden" instrument not a "gator glidden drill". It is also mentioned that the dentist uses it to access the root canal. It is not used to access the root canal but rather to clean and shape it. The proper instrument that is used for endodontic access is a carbide bur.
Crush the sea turtle claims he's 150 years old "and still young." Actually, at 150, Crush would be almost twice the normal lifespan of a sea turtle, which is about 80 years. Contrary to popular belief, not all kinds of turtles have lifespans of over 100 years. It is tortoises, which are land turtles, that are known for their very long lifespans and, even then, the current record is 188 years old, not much older (relatively speaking) than Crush.
When the dentist is scooping Nemo out of the aquarium with the bag, the first time we see the bag it has a zipper top. The next time we see the bag outside the aquarium it is a plain bag with no zipper top.
When the ocean fish all swim down to save themselves from the fishermen's net, part of the wood eventually breaks off as the net falls to the bottom of the sea floor. However in the subsequent shots, the wood is not seen.
Peaches the Starfish has to pull away from the glass tank in order to speak clearly, as her voice is usually muffled. However, when Darla arrives, she speaks clearly without pulling away from the glass.
Nigel, the Pelican, is a Brown Pelican, scientifically known as Pelecanus occidentalis. The movie is set in Australia, where there are no Brown Pelicans, instead there is the Australian Pelican, scientifically known as Pelecanus conspicillatus. Both birds look quite different.
The diving flag seen on the dentist's boat is the United States' "Diver Down" flag (red with white stripe). This flag is not used in Australia, and would not be seen on the Great Barrier Reef. The Australian version is blue and white.
Marlin and Dory are advised to swim to the back of the whale's throat and to be blown out of the whale's blowhole. This is not physically possible as whales mouths and digestive systems are not connected to their respiratory system and blowhole.
The "angler fish" that Marlin and Dory encounter has several characteristics that are not found in deep-sea angler fish. Deep-sea angler fish do not have photophores (the "lights" along the side of the body that are visible when you finally see the whole fish). Also, all deep-sea angler fish have very small eyes, and the fish in the movie has very large eyes (much like a marine hatchet fish). Plus, angler fish are usually found at 1000+ meters, way too deep for Marlin and Dory to survive.
The sharks hold their meeting on what appears to be a World War II-era American submarine sunk by a mine strike. It makes no sense for an American submarine to have struck a mine in Australian waters, since during WWII the U.S. had three submarine bases in Australia and would have been fully aware of any mine fields near the coast.
When Nemo gets flushed and is racing down the sewers, he emerges from below the surface of the water and takes a sharp breath as if he were gasping for air. At several other points in the film (when Marlin is chasing the boat and has to go to the surface to look, and when Nemo is about to leap into the filter of the tank) the animators took care to have the fish go *under* the water to gasp for breath.