Za. Is he really that competent a leader for the tribe, considering he is spending his time trying to make fire instead of helping his people. Also he seems content to keep the TARDIS crew imprisoned even though he is apparently the "good guy" among the cavemen.
Horg. Is he just trying to ensure his survival by offering his daughter to the Chief? Or is he a cunning power-player and the cause of dissent, as shown by him encouraging the rivalry between Za and Kal over who should be leader, knowing that he'll win out.
Broken Base: After the first episode, the fandom is split about how good the next three episodes are. Some people say it's just running around with cavemen. However other people think it continues the themes of the first episode by putting the modern characters in a primitive setting, just as the Doctor was in their era, and enjoy the political intrigue going on among the cavemen.
Hilarious in Hindsight: When Ian and Barbara are discussing Susan's mysteriousness, Barbara remarks on how Susan did not know how many shillings were in a pound, and Susan's excuse was that she forgot that "the decimal system hadn't started yet." The United Kingdom did eventually switch to a system of 100 pennies to a pound in 1970.
Special Effect Failure: Bizarrely, Barbara's first entrance to the TARDIS is much more convincingly realized in the unaired pilot episode. The broadcast version is a lot more jarring by comparison, as Barbara pushes her way into the TARDIS prop, then in the very next shot she, Ian and the Doctor are suddenly stood right next to the console, a good distance away from the doors.
They Wasted a Perfectly Good Plot: The first episode is beloved by many, the next three episodes... not so much. This is unfortunate because the story is built on solid ideas: a tribe of primitive humans starving to death because they lost the secret of fire; scheming politicos in different tribes who make power plays with hostages who know the secret. In more capable hands this could have rivaled "The Aztecs" or even "The Caves of Androzani".
Values Dissonance: The Doctor explains the humans' disbelief of the TARDIS to his granddaughter thusly: "Remember the Red Indian. When he saw the first steam train, his savage mind thought it an illusion too." As though the "savage mind" business wasn't enough, "Red Indian" is generally considered a seriously racist epithet these days.
What Do You Mean, It's for Kids?: The first story has some very sinister sequences, with someone having their chest torn open, and a cave of broken skulls. There's also the implication that Ian and Barbara think the Doctor is molesting Susan.