Clark Gable was considered for the role of Tarzan, but was deemed too much of an unknown to play the ape man.
Apparently, the chimpanzees were supposed to be the baby apes and actors in ape costumes were the adults, a practice that was dropped after this film (one of the men who played the apes was Ray Corrigan).
At no point in this movie is the line "Me Tarzan, you Jane" spoken. When Jane and Tarzan meet, it is she who initiates the verbal exchange, repeatedly indicating herself and giving her name until he repeats it. She then points to him, indicating that she wants to know if there's a word for who he is as "Jane" is the word for who she is, until eventually he understands and says, "Tarzan."
Tarzan's distinctive call was created by sound recordist Douglas Shearer. It was a normal call, manipulated and played backwards.
This film used considerable stock footage from Trader Horn also directed by W.S. Van Dyke, resulting in some very obvious back-projection effects, particularly toward the beginning of the picture.
When Johnny Weissmuller was approached to play Tarzan, he was under contract with BVD to advertise its underwear and swimming trunks. BVD strenuously objected to its spokesman appearing in just a loincloth - the company only wanted him to appear wearing its product. In return for letting Weismuller play Tarzan, MGM allowed BVD to run ads featuring the studio's contract players in BVD swimsuits (including Greta Garbo, Joan Crawford, Jean Harlow and Marie Dressler). (source: "Tarzan of the Movies" by Gabe Esso)