Deliberate mistake: Fritz rescues the mud-trapped zebra and Roberta rides it across the island to the tree house, then again later in the race. Zebras, however, cannot be domesticated or ridden. To film these scenes, Disney & Co. painted a white horse with zebra stripes. (01:20:00 - 01:46:30)
Revealing mistake: In the scene where the logs are rolling down onto the pirates, you are given views of what's happening beneath the logs. Look closely at a pair of flailing feet. The pirate is wearing modern hiking boots.
Continuity mistake: In the beginning when it is raining down on everyone, you get a clear view of the mother's wet, mussed hair. In the next scene, however, it is perfectly dry and in place.
Continuity mistake: While the two eldest boys are getting ready to sail around the island, Francis, the youngest boy, is playing with Rocky, the baby elephant. Francis is on Rocky's back, but in one shot, they are on the beach, near the water, and in the next shot, they are so far in the water that Rocky has to use his trunk as a snorkel.