We finally get to see Earth on the original Trek show, but wait! This is Earth in the 1960s! Wow, those black holes can really do a number on our starships in the 23rd century: one rubber band effect later and Enterprise is being chased by a sixties Air Force pilot aiming to nuke a UFO (nice stock footage). This was the first time travel story from Trek in which we visit Earth of the past (the others were "City on the Edge of Forever" and "Assignment:Earth"). In the latter episode, the journey was made on purpose, following up on the accidental visitation here. This one threads a fine line between comedy and sf adventure. Especially amusing is the female-oriented computer that Kirk is stuck with here and the Air Force pilot's introduction to Spock. And the amusement continues with Kirk's slapstick fight with 3 military officers and their ineffective interrogation. Kirk is at ease here and cool as a captain can be.
On the other side of the coin, we have the pilot (guest star Perry, in fine form), a sixties military version of Kirk, being told he can never go home to his family due to what he knows of the future - well, why did Kirk give him a guided tour of the ship? We know why: Kirk is instantly fascinated by this archaic (to him) version of what will eventually become Starfleet in about 200 years. The pilot is pretty much what Kirk would be if he'd grown up in the 20th century. Likewise, the pilot is fascinated by this glimpse into the future, especially in meeting Spock; he's not repelled as we might expect, overcoming any phobia with the grace that great training and an open mind brings. It's all a playful, colorful adventure - which completely falls apart in the final act when they start transporting/beaming people into themselves - but hey, whatever gets you home.