When the gang is riding the giant bees, Sean identifies the birds chasing them as "white-throated needletails," which is a species of swift. On the contrary, the birds featured appear to be white-fronted bee-eaters, which are in no way related to or resembling needletails.
When Gabato is piloting the helicopter to the island, his hands are in the incorrect position. The cyclic control (stick) would be controlled by the right hand and the collective would be controlled by the left. Gabato is backwards.
When Alexander is translating from Nemo's journal he says the Nautilus is located at the Poseidon Cliffs. Yet, later in the film Alexander tells Hank and Sean to go a mile and a half in a particular direction towards the Trident Cliffs where the submarine Nautilus is located.
The helicopter in Palau has a registration number that begins with N. This indicates it is registered in the United States. Palau as part of Micronesia would have an aircraft registration beginning with V6.
At the very end of the movie as it zooms out from the Earth to the Moon, along the way we see airplanes and satellites, and just before the Moon we apparently pass through some sort of asteroid belt. There is no asteroid belt between the Earth and the Moon.
After Sean falls from the giant bee and injures his ankle against a log several individuals say he has a "dislocated ankle" and his stepfather and grandfather reset it quickly and easily as you would do with a dislocated shoulder. Although it is possible to "dislocate" your ankle it is not only very difficult to do, but due to the unique, and very stable, make-up of the ankle (unlike the shoulder) it only occurs in conjunction with either a fracture or multiple ruptured tendons of the area. Something that is very serious and extremely painful and definitely not something that could be easily remedied by 'popping it back into place' and then the individual being able to walk about and hike.
The Nautilus would have been out of oxygen by the time that Hank and Sean made it to the submarine. Submarines are not made to stay underwater for a long time before they have to return to the surface to exchange the stale air for clean oxygenated air. And, judging by the fact that the Nautilus was submerged for 140 years (or at least that's how old the batteries are, according to the movie), all of the air on board would be extremely stale air and the movie characters would not have survived for very long.
When they land on the (uninhabited) Mysterious Island, the sand over the half-buried Gabby is patted down nicely; but there are large numbers of footprints around him on sand that should be smooth except for the footprints of the other three.