The biggest inconsistency in various retellings of the Arthur story centre around the mother of Mordred, Arthur's child by incest, and most of the key inconsistencies seem to centre around the women in the tale.
Accepted canon has Morgause (or Morgawse) as the mother of Mordred, and presents Morgause as the illegitimate daughter of Uther Pendragon. In many versions, Morgause goes on to marry King Lot of Lothian and have four other sons: Gawain, Gaheris, Aggravaine and Gareth. Marion Zimmer Bradley however casts Morgause as sister to Igraine (Ygraine), Arthur's mother. Morgause is sometimes credited with poisoning Merlin.
In other retellings Morgan Le Fey is cast as Mordred's mother. My suspicion is that this is generally done to cut down the cast list, but I may be being ungenerous. (Although, it is worth noting that this is most often done in film or TV versions, so maybe I'm not being ungenerous). The best known book in which this casting appears is Mists of Avalon by Marion Zimmer Bradley. Morgan, also known as Morgana le Fey is either presented as Arthur's younger full sister (in which case she is not the mother of Mordred) or as the daughter of Igraine and her first husband Gorlois king of Cornwall. Morgan also steals Excalibur and gives it to her lover Accolon to fight Arthur with.
Guinivere is also subject to inconsistency -- It is often presented that Arthur had two, or even three wives named Guinevere (or Gwenyfahr or other variations). All the legends have her abducted, most commonly by Melwas (Meleas, Melageant etc.) King of the Summer Country, although there is a grey area around whether or not she is actually violated in the course of the abduction. Guinevere's affair with Lancelot is a later addition to the story, possibly Victorian, although possibly much earlier.
The story of the maiden who is
Merlin's downfall also varies widely. Her name is given variously as Niniane, Nimue and Viviane, and she is either the Lady of the Lake or one of the Maidens of
Avalon. In some legends she locks him alive in the trunk of a tree, in others in a cave. As an aside, in Bradley's version 'Merlin' is a title, rather than a specific person.
The other key inconsistency is around who orders the killing of male children -- consistently all male children between a certain age are set adrift in boats to drown, in an attempt to kill Mordred, however in some versions it is Arthur who orders the atrocity, in some Merlin and in still others Lot.
The modern book most closely aligned to older legend (and my personal favourite retelling) is Mary Stewart's Merlin Series, The Crystal Cave, The Hollow Hills and the Last Enchantment. A fourth book, The Wicked Day centres on Mordred and the end of the legend, but is less close to older versions of the myth