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.
Other mistake: On some VHS editions of this episode, the back cover features a picture of what appears to be both good and evil Kirk sitting at a table, however this never happens anywhere in the episode. That picture is actually from the episode "What Are Little Girls Made Of?"