Deliberate mistake: When Tarzan fights with the leopard, it scratches his chest. However after they fall into the pit and Tarzan comes out carrying the dead leopard, the scratches on his chest have amazingly healed. [It is a long-standing Disney tradition that no evidence of violence is shown on screen. Still a mistake, but there's why].
Factual error: When the humans are capturing the gorillas, Clayton fires about 15 rounds from his double rifle. This is pretty impressive, considering this is the early 1900's.
Continuity mistake: After Tarzan fights the leopard, and at the point when the gorillas and him run off, the dead leopard is missing.
Continuity mistake: When child Tarzan jumps in the lake with the elephants the water is only up to the elephants' feet, but the underwater shot shows the elephants swimming.
Continuity mistake: When Jane snatches her drawing back from the baby monkey she tucks it into her belt. The picture disappears while she is being chased by the fleet of baboons. The picture returns again after the chase before Tarzan snatches it to return to the baby monkey.
Continuity mistake: When Tarzan decides to become the new leader of the apes, his hair is waving in a strong wind, but the rain is pouring straight down.
Factual error: During the song "You'll be in my Heart", lemurs are shown in the tree that Kala and baby Tarzan are in. "Tarzan" is set somewhere in Africa's equatorial jungle, as this is the only place gorillas live. Lemurs are native to the island of Madagascar.
Continuity mistake: When Clayton is drawing on the chalkboard his shotgun is leaning against it. After Tarzan takes the chalk and draws all over the chalkboard, the gun has disappeared.
Continuity mistake: When Tarzan says "A hair?" and Terk replies "Yeah, a hair", their hair is blowing in different directions with the same current of wind.
Continuity mistake: As young Tarzan fixes his spear, he's sitting on a moss covered branch, and just behind him on his left is another branch growing from the one he's sitting on. After the shot of the yellow fruit, it returns to Tarzan. Assuming he hasn't moved from his spot, the branch that was behind him should still be there, but isn't.
Continuity mistake: In the scene where Jane is telling her father about Tarzan, and Clayton calls it a "girlish fantasy", Tarzan jumps into the camp. Throughout the entire scene, Jane's hair was slightly tied back, but when Tarzan comes very close to her and says "Jane", it's down. The next shot it's slightly up again.
Plot hole: Kerchak is mad with Tarzan because he showed Jane, Porter and Clayton to the gorilla's current location. Yet he does not move the group even though he obviously knows they're no longer safe there.
Suggested correction: He does actually move the group later on in the movie. Then they get ambushed by the hunters and he is killed.
Continuity mistake: During the fight with Sabor, Kala receives two claw marks on her right cheek. Later, when she reunites with the gorillas, the claw marks are gone.
Continuity mistake: When Sabor's right leg gets caught in some rope, her tail disappears. When Sabor is seen tangled up in rope, her tail reappears.
Continuity mistake: When Sabor attacks Kala and Tarzan, her ears change from black and white to yellow and white when she focuses her attention on Tarzan and to black and white again when she jumps off Kala.
Continuity mistake: After the elephant stampede, Tarzan apologizes to Kerchak, whose left hand is visibly about a foot and a half from him. But in the next shot, when Tarzan attempts to touch his hand, it's only a couple inches away.
Continuity mistake: When Tarzan brings the group to where the gorillas are and they come out from hiding you can see the biggest Gorilla in the middle looks exactly like Kerjack, at a point when Terk and Tantor are suppose to be distracting Kerjack away from the camp.
Factual error: The weight of an elephant is nowhere near that of a large cargo ship so even if Tantor was able to climb up the side of the ship the ship shouldn't have moved.
Suggested correction: Is there different rules in the cartoon world and live action? Animals getting smashed flat then getting up like nothing happened.
It would entirely depend on the specific cartoon. Not all cartoons have a consistent logic. Ex. Sure, a character might get flattened then get back up in a Looney Tunes cartoon... but you'd never see that happen in "Akira," which is also a cartoon. If memory serves, "Tarzan" follows a loose realism when it comes to things like logic and physics, so a mistake like this would be valid.
Deliberate mistake: Throughout the first part of the movie, Tarzan and all the other animals are speaking to each other in English. After Tarzan meets Jane, he has trouble communicating with her and later shows her that he communicates with the gorillas using grunts. This means that the earlier communication between Tarzan and the animals was done for the benefit of the audience. However, with this being the case, Tarzan shouldn't have been able to tell Jane his name, since the gorillas communicate with him in grunts, they would have had no way of vocalizing a name for him that could translate into a human language. At least not until Tarzan and another human could agree on what his name should translate to.
Continuity mistake: When Tarzan is climbing the tree as "Son of Man" starts, the continuity of the bark, vines and moss on the tree doesn't match between shots. Example: Just before he begins to climb, there's no bark on the tree. When he reaches up, there's bark. After he slips, he stops in a barkless area, but it's the same area where there should have been vines and moss as there was previously. After Kerchak passes him, there's more bark on the tree than there was in the previous shot, and so on.