Shore Leave - S1-E16
Character mistake: Yeoman Barrows is a crew member on an star ship and I assume has experienced or has trained to experience many different things she will encounter on the tour of duty but she freaks out and cries uncontrollably just because she sees Don Juan.
Character mistake: Spock tells Kirk that without being able to test their vaccine with the ship's computers, "it could be a beaker of death." The vessel that the vaccine is contained in is a flask, not a beaker. The ship's science officer should know the difference. (00:37:25)
Character mistake: Kirk is surprised by Spock's behavior, but shouldn't everything about Spock be in his records? Kirk should therefore know about Spock's needs and have planned for them.