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.