3. Balance Of Terror (Episode 14)
The Plot: The Enterprise and a Romulan ship battle one another.
The Screw Up: This episode is an homage to submarine thrillers, specifically The Enemy Below and Run Silent, Run Deep (not to be confused with the porno of the same name.) There's a scene where both the Enterprise and the Romulan ship power down and play dead, waiting for one to make a move. While this is happening, both crews whisper to one another. This is a common trope in submarine films, where everyone is dad quiet hoping to avoid detection from an enemy ship. However, this is Star Trek, and it's in frickin' space. It's stupid.
Cool Trivia: This is the first appearance of the Romulans!