Complete Monster: Queen La is the mystical queen of Opar, who created and enslaved a race of leopard men from mundane leopards. La has a bad habit of incinerating her followers who cross or fail her, and a history of killing men who reject her. When Professor Porter is brought to her, she decides to have him sacrificed before she falls for Tarzan; attempts to kill Jane; and later tries to sacrifice Tarzan for rejecting her. In her next appearance La's leopard men start to rebel against her and try to place Jane as the new queen to free them; after La gets back into power, she executes some of the leopard men but plans on doing something special for the leader of the rebels—attempting to feed him to a monster. During the next battle, La incinerates more of the leopard men, and when Tarzan is seemingly killed, mocks Jane about it. Despite La's death, her spirit later returns and possesses Jane in an attempt to get her power back. During the final fight against her, La possesses Tarzan and muses at the prospect of killing his beloved wife using his own body.
Genius Bonus: The titular leopard cub of Tarzan and the Lost Cub is obviously supposed to be Jad-Bal-Ja, the Golden Lion. With Sabor having gone from lioness to leopard it makes a certain amount of sense.
Harsher in Hindsight: "The Trading Post". Tarzan must find the rhinos a new home when the trading post drives them into gorilla territory. The conflict is solved but with a Bittersweet Ending:
Kala: But with more and more people coming to the jungle, I can't help but wonder..
One episode has Tantor state that "they ought to put warning labels on [scary books]". Nowadays, certain books do have parental advisory stickers, and even ESRB-style breakdowns of objectionable content.
When Tarzan and Professor Porter try to stop Professor Philander from caging (and he plans on killing too) the silver ape Mangani, he cuts a rope Tarzan was hanging on, sending him falling several stories to his apparent death. Rather than let Archimedes examine and try to save his son in law, Philander plans on stranding him at sea and tossing Tarzan's body overboard.
Lt. Colonel Staquait crossed it by ordering Hugo and Hooft to burn a village full of civilians that he knew included innocent women and children. AND to top it off he tried to have them executed for daring to object to this atrocity calling them deserters.
They Wasted a Perfectly Good Character: The leopard cub and his mother who end up befriending Tarzan and his family in "Tarzan and the Lost Cub", making them the first predators to serve as friends to the protagonists instead of random adversaries. The idea of "good leopards" who could have been recurring allies and companions to Tarzan (similarly to his lion companion Jad-bal-ja from the book series) definitely had a lot of potential, but alas they never appeared again after their debut episode.
Dania from "Tarzan and the Rift". In that episode, Tantor gets the chance to ask Dania out on a date, but the evening gets ruined by Terk showing up, making noise with household items, and being oblivious to the other characters' feelings. At that point, Dania being alienated by Terk is justifiable. To make matters worse, this is all just a big misunderstanding. The whole conflict could've been avoided if Terk had just apologized to Dania for making such a bad first impression, or at least done something nice to make up for it. But instead, the episode acts like Terk's actions were automatically forgivable. The episode never acknowledges the misunderstanding and expects us to dislike Dania for believing that Tantor should stop hanging around with Terk, despite the fact that her belief is based on Terk making a bad first impression and doing nothing to make up for it. On the other hand, she meant well the whole time, until she thought she would lose a friend. Dania simply said Tantor had to choose between his best animal friend or her, when she could have said "Wherever we go, don't let her anywhere close to me!".
Philander at the end of "Tarzan and the Missing Link". This is mostly because of all the protagonists taking a level in jerkass by being unnecessarily harsh to Philander. Also, Philander only brought those two men to Africa because they were threatening his life. Porter should've at least been respectful while rejecting Philander's offer at the end, instead of literally roaring in his face. However, Porter's attitude becomes much more forgivable if you know Philander has already been established as a deceitful and greedy scientist, especially in "Tarzan and the Silver Ape" before this episode, where Philander crossed the Moral Event Horizon by almost throwing Tarzan to his death... So Porter is understandably fed up with his antics.
Harsher in Hindsight: One of the TV spots features a gorilla carrying an infant Tarzan out of a cradle. This began airing shortly after an incident at the Cincinatti Zoo where a gorilla named Harambe was shot dead after grabbing a small child who fell into his exhibit.