I don't what kind of car it is, but there's a photo of Captain Kirk posin' with a big pimp car at http://www.monstersandrockets.com/2009/05/60s-trek-candid-shots.html
It sounds like it was some sort of inside joke on the Trek set to have the guys pose in costume beside their rides.
Skipweasel, bear in mind that this is a test from 1983, so this film version of "Where the Wild Things Are" was never completed. The film version Spike Jonze is making could be terrible, but from what I've seen it's clear he really respects the book. That's a lot more than you could say of the directors of movies like the Mike Myers version of Cat in the Hat.
It sounds like it was some sort of inside joke on the Trek set to have the guys pose in costume beside their rides.