Guest stars:

Warren Stevens          Rojan
Barbara Bouchet         Kelinda
Stewart Moss            Hanar
Robert Fortier          Tomar
Carol Byrd              Lt. Shea
Leslie Dalton           Drea
Julie Cobb              Yeoman Thompson (crushed and killed while in crystaline form)

Crew appearances:
Kirk, Spock, McCoy, Scott (only ones to not get the zap)
Lt. Leslie
Uhura
Chekov
Nurse Chapel
No Sulu
 
Answering a distress call, the Enterprise crew find themselves lured into a trap by the Kelvans, aliens from the Andromeda Galaxy who have assumed human form. The Kelvans commandeer the starship, reduce the crew to crystalline blocks, and head for Andromeda, where they plan to organize their race to take over our own galaxy. Can Kirk and Spock save not only the Enterprise, but the entire Milky Way Galaxy as well? But of course.

Kelvin: (Kelvin Empire) in the Andromeda galaxy, due to a threat that radiation in Andromeda life there will be impossible so they are searching for habitable galaxy to conquer and occupy.

Kelvins: non human, emense beings with 100 tentacles, without emotion or sensation. When assuming human form are baffled and confused by human emotion and feelings.

Unnamed planet: no life forms, purple sky, vegitation

Neural field paralyzer: worn on the belt. suspends animation, reduces humans to their crystaline form.

Dibernium: a metal that is similar to the jail bars made by the kelvins (altho the jail bars are more dense)

Aminiar 7 mentioned: the Vulcan mind probe used to escape jail their too, but this time Spock is thrown across the room. However, he does get an impression of what the Kelvins really look like. (see A Taste of Armaggedon)

Kirk uses a Karate chop to subdue Kalinda (a 1960's ploy you dont see very often on TV anymore, but I remember that being a feature in a lot of drama on TV in the 1960's)

Note:
3D chess set is shown
Saurian Brandy is drank
Energy barrier at the end of the galaxy looks like high speed aurora borealis.

Mentions Shakespear: That which we call a rose by any other name would smell as sweet.

Vulcans have the ability to put themselves into a trance, more restful than a so called vacation.

Formazine: an injection given to Tomar to make him climb the walls

Stokaline: medicine given to Spock to make him come out of this trance, but its must be a ruse because Nurse Chapel protests and almost gives it away.

Rigilian Kasaba Fever: mentioned as the ailment Spock has

Sashire: Kelvins word for crystaline shapes similar to flowers

Quotes:
"You have a very strange sense of humor." Kirk
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"Mr. Spock, you're sick." Kirk
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"It's green." Scotty
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"We did it. you and me. Put him right under the table" Scotty.