Continuity mistake: When Uhura's rescue party is in the transporter, Chapel's uniform is blue. When they materialize on the planet, it's red for a moment, then blue.
Beyond the Farthest Star - S1-E1
Continuity mistake: There is an alien in a Starfleet gold shirt sitting next to Sulu. For a second, there is a human in a Starfleet red shirt, then it goes back to the gold shirt alien.
Beyond the Farthest Star - S1-E1
Other mistake: When showing Scotty on the bridge, some of the frames show more of his body than others. In those frames, you can see that he lacks legs.
