What kind of car is this behind Mr. Spock?

Per this pic

Looks like an Izismile X-Monkey to me.

I believe it’s called a “flivver.”

In other words, your link doesn’t work. Or, “Reply hazy, try again later”.

Looks like about a 1965 Buick Riviera. See this pic on Wiki:

Based on what wiki says it could be from '63 to '65, I don’t know if someone more familiar with them than I am could tell any closer than that.

1963 Buick Riviera

After seeing the simulpost by RJKUgly, I did a little investigating, courtesy of eBay Motors.

The '63 and '64 have nearly identical front ends. I can’t tell the difference.

The '65 was a complete redesign with double headlights that were stacked on top of each other.

So it could be a '63 or '64.

I checked some other Buicks, but this is the only one that didn’t have a Buick grill ornament right in the middle.

I believe the Riviera was marketed as it’s own make, or maybe Riviera (by Buick). They were sold by Buick dealerships, but didn’t have the Buick emblem anywhere on them.

Tarsier, actually.

If he’d gone for a Chrysler Cordoba, a co-star could have offered him some soft Corinthian leather.

That is definitely a '63 Buick Riviera.