If that's the worst TOS contradicts itself, I think the series did okay. Especially as a lot of them are easily explained.
Spock claimed Sarek was his ancestor? That's not a mistake, it's technically correct... the best kind of correct for a Vulcan. Uhura changed departments? That's a thing officers do. Pike's age was contradicted in the very next line, so that's just a mistake. The ship used contradictory stock footage of the ship within the same episode... yep, they didn't have the money to do better, it was flaw in the production, not a later retcon.