That sequence with the cop appears to be footage that was originally filmed for a first season episode, probably "Las Vegas". The boys are in what looks like the same car ('49 Buick?) they bought from Friendly Fields in that episode. Bud Abbott appears thinner and Lou has that pasty- overly made-up look that was typical of the later first season episodes. What the whole "Mr. Bronson's (Milt?) wife and her daughter" bit is all about was most likely explained before that whole part of the episode was edited out, only to have this brief part tacked on to this episode.

Perhaps the part where Lou is giving Bud a rub down and is mistakenly following radio broadcasted instructions on how to paint a car is the part Lou had something to do with as far as coming up with parts of the bit. It's a sequence that is very similar to one they did live at almost the same time for a Chistmas 1952 Colgate Comedy Hour broadcast where Lou is supposed to give Abbott a scalp treatment but Sid Fields (again) is giving radio instructions on how to stuff a turkey!