There are numerous plot inconsistencies.
In "The Squire of Gothos" (first season), they hadn't yet decided how far in the future the story takes place. Trelane's planet is about 900 light-years from Earth. He's reproduced an Earth-like environment from roughly 200 years before the present (he mentions Alexander Hamilton). An officer mentions that it's as if he's been observing Earth through a telescope -- implying that the episode takes place about 700 years in the future, very roughly 2660.
In "Tomorrow Is Yesterday", Kirk is at a US Air Force base in the 1960s. Lieutenant Colonel Fellini threatens to lock Kirk away for two hundred years. Kirk says, "That ought to be just about right" -- implying that the episode takes place about 2160 or so. (That episode was aired just 2 weeks after "The Squire of Gothos".)
In "Obsession", Lieutenant Leslie was killed by the cloud creature. He appeared, alive and well, in a number of later episodes, all the way to the end of the original series.
In "The Conscience of the King", Spock mentions that his father's planet was spared the dubious benefits of alcohol. McCoy replies, "Now I know why they were conquered". In the rest of the series, there's no indication that Vulcan was ever conquered; in fact, in "The Immunity Syndrome", Spock says that Vulcan has never been conquered in its collective memory.
And so on.