When Apollo is first taken into sick bay he has a full head of grey curly hair, (wig), later when Kirk goes to see him in sick bay he is missing the wig and is almost bald, this remains the case for several scenes, later when Spock calls Kirk to the recreation room Apollo has a full head of grey hair again, (wig is back ). :o)
When Kirk carries the unconscious Uhura into Sickbay and places her on the biobed, her head slumps off to her right on the pillow. In a subsequent close-up, her head is straight and she's facing the ceiling. The following wide shot shows her with her head slumped off to her right. And then, after the life-sign monitors show that she's dead, her head slumps off to her left.
When the Enterprise is shown firing the photon torpedo at the object in the opening scenes there is some sort of large satellite visible in the shot in front of the enterprise, probably from a set up from a different episode FX shot.
When talking to Sulu over the communicator, Scotty pronounces the word "err" as "air". This is a common mistake made by (my fellow) Americans. Scotty would have used the correct pronunciation, which sounds like "er".