Jaguars don't generally live to be over 15 in the wild, and the oldest jaguar in captivity was recorded to be 23. It is highly unlikely Sabor, already an adult at the beginning of the film, would still be alive approximately 20 years later to fight Tarzan.
Clayton speaks of having been in Zambia. Zambia at the time of this movie was divided into two regions called North Western Rhodesia and North Eastern Rhodesia, Southern Rhodesia being what is today Zimbabwe.
Professor Porter and Jane offer to take Tarzan to England where he would meet Darwin, Queen Victoria, and Kipling. Charles Darwin died in 1882, the same year in which the yet-to-be-published 17-year old Rudyard Kipling finished college and returned to India.
When Tarzan first meets Jane, after saving her, he tries to communicate with her. Living all his life in the jungle he could not be familiar with any human language, though he pronounces his name in English.
Jane has the picture of the small baboon tucked into her skirt at the start of the big chase scene where she is rescued by Tarzan. All through the sequence the picture is missing and then at the end when the baboon is descending on the parasol the picture re-appears tucked into her skirt again.
When we first see Clayton, he's slashing down bamboo stalks with his machete and there's a large nick in the blade, close to the handle. As soon as he places the machete in his belt, the nick in the blade is missing for the rest of this scene.
Tarzan takes place in Africa, but Sabor is clearly a jaguar, a big cat found only in South and Central America. Most likely the makers of the movie intended to portray a leopard. Jaguars, however, have larger rosettes which contain smaller black spots whereas leopards are marked by smaller, empty rosettes. The two animals can also be distinguished by the way they are built, with the jaguar being a heavier built cat with a broader head and shorter tail than the leopard.
The gorillas that raise Tarzan are mountain gorillas, which are only native to Uganda and Rwanda. These countries are not on the west or east coast of Africa, so they should have been western lowland gorillas.
When Terk uses typewriter in the camp, the carriage moves in the wrong direction (from her left to her right). The carriage is also seen to return automatically which is not correct for a manual typewriter.
During the fight scene in which Tarzan kills Sabor, Sabor scratches Tarzan's chest. The scars are there momentarily and in the next camera shot are gone, then reappear, then disappear. The director's realized the scars would become cumbersome and therefore decided that Tarzan would heal miraculously fast. Humorously, Disney was later contacted regarding the production of a "fast-healing Tarzan action figure" due to this scene.