The Aztecs continues the trend of the true historicals in Season 1 being better than the sci-fi stories. The four part length of the story coupled with John Lucarotti's faster-paced script helps this; but also this story introduces a number of elements that Doctor Who would use later on.
The TARDIS crew lands inside an Aztec tomb of Yetaxa - a fictional Aztec high priest-cum-God, with Barbara having studied the Aztecs being particularly interested. She find the secret exit from the tomb having picked up Yetaxa's bracelet and therefore is immediately considered to be a God reincarnate and the others in the TARDIS crew her servants. Ian is sent to the barracks to be a contender to lead the Aztec army (challenging Ixta, the long-time leader); the Doctor to the garden as an elderly man living out his last days while Susan stays with Barbara initially - until she intervenes in a human sacrifice attempting to change history where she loses the trust of Tlotoxl, the High Priest of Sacrifice, who then sees her as a false god. From then the main story is about getting back inside the tomb to the TARDIS while retaining the support they have - in particular from Autloc, the High Priest of Knowledge - to last as long as possible.
This main thing this story adds in is the point that you cannot change known history - as the Doctor tells Barbara: "you cannot change history, not one line!". That is the main point of this story: Barbara who is featured heavily as almost the main character (being a God) attempts to try and change things to ensure that her beloved Aztecs survive only for that to only cause problems for them: Susan is taken to a seminary to learn Aztecs ways and they lose trust of key people in the civilisation. This is something that becomes important throught Doctor Who and I think this is a perfect introduction of the concept simply because it makes sense why Barbara would want to try and change things; but also historically why it cannot happen. Jacqueline Hill does a great job playing Barbara here in, alongside the Keys of Marinus, some of the main stories that features Barbara in a major capacity.
It also features some of the early signs of romance involving the Doctor, who accidentally gets engaged to Cameca, an older Aztec lady. Its clear that the Doctor does have some sort of affection there which adds to this - and really its one of the few examples in the classic series of this sort of theme being explored which makes it remarkable that its in one of the early stories.
The production is very good - considering the overall budget the sets appear as convincing as you'd expect. It also feels like an authentic characterisation of the other cast members - while Tlotoxl is clearly the villain of the piece his reasons for being so make sense - his core beliefs are being challenged by a set of people who are, in fact, being dishonest themselves and as we know Barbara is not in fact a God he has no reason to trust her; and while Aztec beliefs are not ones that we would follow; it would take more than being preached to by a random outside to trust them. Autloc is the voice of reason on that side - but his reward is to simply lose his faith in the core Aztec teachings and leave the city while Tlotoxl retains his power; so there's a strong argument that Barbara's intervention was in fact harmful. While a lot of stories have a clear hero and villain; this feels surprising nuanced for early Doctor Who.
In terms of negatives; this is another story where Susan is sidelined - admittedly Carol-Ann Ford was on holiday for two weeks in the middle of filming which is a factor in this; but she spends her time being treated how to be a good house wife and almost being married off to the Perfect Victim - which considering recent stories adds onto her being misused.
Overall - this is a very good, engaging story that while not perfect is a highlight of early Doctor Who.