Continuity mistake: Early in the movie when Thomas falls overboard, John Smith ties a rope around his waist (00:02:56) and jumps in after him. Thomas is very far away from the ship (00:03:12). But when the men pull John and Thomas up, John is holding on to the rope with one hand and the end is left dangling (00:03:36). One of the men who pulled them up then coils the rope with a mere two coils (00:03:48), not nearly long enough to have reached Thomas while he was overboard. In the same scene, when we are viewing the men pulling John and Thomas up from above (00:03:38) there is no extra rope at their feet as there should have been for such a long rope.
Other mistake: When Percy sees Meeko in the bubble, it is done in first person perspective and we can see straight through the bubble, showing that Meeko is not there on the other side.
Continuity mistake: When Pocahontas sees John Smith for the first time, John is climbing up a cliff face and then a tree. You can see his musket strapped to his back as he's climbing. But after he tells Thomas he's getting a better look and then is shown in the tree, his gun has vanished.
Continuity mistake: When Meeko follows Pocahontas by jumping off the cliff, he accidentally knocks Flit, causing the bird to spin upside down. But in a wide view of the cliff in the next shot, we can see Meeko but Flit is nowhere to be seen.