Good grief, did Carol Burnett ever age in the 20th century? She was in her late fifties in that sketch..!
That was great. Re: the set, the whole thing was built with wood and rented greeblies from the props warehouse. So the walls and upper displays would have been easy to build with standard shapes and backlit pictures, while the actual controls and stuff would have been impossible to replicate on a variety show budget. So they just used whatever they could to approximate starship buttons and panels and stuff.
Also, look at the Captain's chair! A few years later we'd see it on the bridge of another starship, at about 1:40 here: