Several times throughout this episode they refer to "Starfleet Control" instead of "Starfleet Command."
The Enterprise's chronometer, used in this episode, is mechanical with an odometer type display. This is a rather primitive device given
twenty-third century technology and the Enterprise being a state-of-the-art starship.
When Spock is doing the countdown for beaming Christopher back into his plane after going back in time again his counting speeds up once he gets to around 5.
Why was Captain Christopher standing up when they beamed him on board? Wasn't he sitting in the jet?
Why do Sulu and Kirk beam down into the Air Force base in standard Starfleet uniforms? On later such missions (Assignment: Earth -
Patterns of Force) they have suitable clothing made up, but here they just stand out like sore thumbs. And if they want to be sneaky, why don't they wear black stealth-type clothing?
When the Airforce guard said to Kirk "I'm going to lock you up for 200 years!" then Kirk said "That ought to be just about right.", actually 200 years after 1968 would be 2168, not 2268.
Kirk introduced Spock as a Lieutenant Commander when actually Spock is a full Commander.
In the scenes with the Enterprise shaking in space you can see a lighter space background than on the rest of the screen.