I noticed in Forgotten Lady, there are a couple scenes where the butler and his wife are watching Johnny Carson on tv and i think it's even mentioned by Columbo at some point. Is this a shameless plug or just referencing popular culture at the time. I think Columbo was on ABC in the 70's, while Carson show was NBC if i'm not mistaken (so did they have to pay or get permission to air?)

It's a fun reference, and yes a cultural touchstone at the time, but I don't know if I would consider it a plug for NBC as such -- although possibly a plug or tribute for Johnny. Peter Falk was on Carson's show many, many times, and they seemed friendly to each other. Here's an (audio) example, from Carson's "Best of the Tonight Show" LP set:

https://www.youtube.com/watch?v=STOrR_0qK7A

At the time NBC was still the sole owner of the Tonight Show so they had control over whether any footage could be used. Johnny didn't gain ownership of his program outright until his big contract renegotiation with NBC in the late 70s.

That particular program they used on the special, I remember looking up in the Carson database that used to exist on-line (it's not there any longer) was a program that aired on a Friday interestingly (we in fact even see Johnny's signoff where he says that on Monday Steve Allen will be guest hosting!), and that contradicts the internal references in "Forgotten Lady" which I believe had the next day being a Friday!

I haven't seen it in a long while, but it has more pop culture references than many episodes. There's Army Archerd playing himself, something that almost never happened on COLUMBO (which I'm glad about, since that idea gets out of hand on most shows). And of course, there's that excerpt of an actual Janet Leigh musical (I can't think of its name).

The real movie's name is the same as in the episode, "Walking My Baby Back Home" (though in the episode they only call it "Walking My Baby"). Though in the actual film, Janet's character name was Chris, not Rosie (they were likely tapping into her playing Rosie in "Bye Bye Birdie" for that detail).

Of course there's the scene at the studio where the Jaws shark appears and Columbo asks if that's the shark from the movie.

Grant said:

"There's Army Archerd playing himself, something that almost never happened on COLUMBO (which I'm glad about, since that idea gets out of hand on most shows)."

Nice observation, and one I'd have liked to agree with, except it happened just enough to provide a lot of annoying memories. Several awkward moments that come to mind:

In "The Most Crucial Game", there was a couple of minutes of "fill" with some basketball players shooting hoops (including a very young and non-greased-down Pat Riley). Edith Head appeared in "Requiem for a Fallen Star", and seemed to have trouble not tripping over Anne Baxter's lines. And perhaps the most annoying was the group of poker-playing has-beens in "Uneasy Lies the Crown".

And who can forget Little Richard in "Murder of a Rock Star?"

I can't help agreeing with those (except that I think Edith Head was at least worked into that scene A LITTLE "smoothly").

One comical thing in my case when it comes to that basketball scene is that I immediately recognize one of the names from being an OUTER LIMITS fan as opposed to a basketball fan, because Leroy Ellis played an eight foot tall space creature in an Outer Limits episode!