I would love to have more context for this since I know little or nothing about it. I've seen this clip before , it is without a doubt as strange as anything I can think of seeing on TV short of what Andy Kaufman has done. At any rate C Glover is something else, nice find.

I heard about this incident many times, but I had never seen it until today.

I suspect that the joke is on Dave, but he just doesn't get it, or can't take it.

From wikipedia "In 1987, Glover appeared on Late Night with David Letterman to promote his new movie River's Edge and his album. Dressed as his character from the film Rubin and Ed, he wore a long wig and platform shoes. His bizarre appearance was exceeded only by his strange behavior, which was thought by some to have been influenced by drugs, while others presume it was an Andy Kaufman-style stunt. After a failed attempt to challenge Letterman to an arm-wrestling match, Glover delivered an impromptu karate kick just inches from Letterman's face while shouting, "I'm strong... I can kick!". A noticeably irked Dave abruptly ended the segment and cut to commercial. Glover has later commented, on The Adam Carolla Show and Tom Green Live among others, that he neither denies nor admits any of the rumors surrounding the incident.
"
Strange fellow.

Speaking of Crispin Glover strangeness, in case you haven't seen it, here's the trailer for his film What Is It (definitely NSFW and possibly disturbing and/or offensive). He was or is touring the country with it, screening it with an introduction and audience Q&A. Saw it at the Castro in SF about a year or so ago . . . I admired the film's taboo-breaking bravado, but wasn't terribly impressed. Crispin Glover himself was quite charming, well-spoken, and sincere.

Oh geez, how did I mess up that link? Here it is again. The trailer for What Is It? (again, NSFW, possibly disturbing and/or offensive).

I assumed it was an act and that Letterman was in on it. Guess not.

Here was his return to Letterman. If you start reading from this comment on, you'll learn a lot about good ol' Crispin.

He was doing a character, kinda. He doesn't like to talk about it now though. If you watch his Clowny Clown Clown video, you'll see the character again.

That video won't load for me, but:

I saw the original full broadcast. If Crispin Glover intended it to play as as performance art, it was, um, poorly framed. I and my proto-hipster friends, arguably the target audience for underground performance art a la Andy Kaufman, pretty well concurred at the time that perhaps at the outset Glover meant it to be cool or wackily charming or a character piece, but somewhere along the line he just came thoroughly unglued.

I vividly remember watching alertly, trying to make sense of whatever kooky antics were afoot, but Dave's expression and the sudden cut to commercial confirmed my impression that this Was Not Comedy. Like, not even guerilla comedy. Or at least not well-executed guerilla comedy.

Here's another disastrous Letterman interview with Harvey Pekar. I can't find the one that's referenced in the movie American Splendor though, I'm guessing it's been well squashed.

More on the Pekar incident. This fascinating 1988 article was written by Pekar himself, under a pseudonym.

Fascinating indeed. I can however see both sides of the story, as it ends up being pretty much "manipulate the manipulator".

I miss old television. Before everything was spit-shined for the camera and everyone had blue-white teeth and composed themselves for mass consumption. It's what makes me love old Love Connection reruns so much. People were themselves, flaws & all. It's more entertaining.

So while it was hard to watch the Pekar clip, it was refreshing to see Dave being human. I think the only time I've seen him do that lately was when he insulted Bill O'Reilly.