The theme song used on the DVDs is not Billy Joel's "My Life" but the theme that replaced it in most syndication versions: "Shake Me Loose," a vocal version of the closing-credits theme. "Shake Me Loose" actually was written by the series creator, Chris Thompson, and it appears to have been the song he wanted there in the first place (to get royalties, if nothing else). But I realize many people strongly associate "My Life" with this show and may be disappointed that it's not there.
As always, the best parts of the show are the ones that have the least to do with the ostensible premise of two guys dressing in drag. As the season goes on, the drag element was de-emphasized, and by the second (and better) of the two seasons, they would go whole episodes without donning the dresses. It's not just that Hanks and Scolari were funnier in their own clothes, with the freedom to ad-lib and make up physical business -- the women's clothes restricted their feedom to move around. But as this mini-history of the show mentions, the elaborate costume changes slowed the show down and killed the spontaneous feel that made it fun:
"They made up a lot of business," says [staff writer Leonard] Ripps about the duo's repartee. "They were very active in suggesting ideas because they're very creative guys. The drag was the most difficult part of the show. They tolerated it for a season. It's just a problem doing a half hour of drag every week. It took a long time getting them in and out of wardrobe, which meant it was tough maintaining any kind of momentum in front of a live audience."
The thing about the very loose, free style of Bosom Buddies, which allowed even so-so scripts to be elevated by the cast's energy and improvised bits, is that it's a kind of style you don't see in multi-camera sitcoms today. A lot of them tend to be stop-start affairs where the actors do a lot of takes, hit their marks robotically, and don't get the filming done until late at night. Which may be part of the reason why multi-camera, live-audience shows are dying out: what's the point of doing them if not to let talented comic actors cut loose in front of an audience?
I hope the first season sells well enough to justify the other season coming out; that's the season that has the real gems, like the flashback episode to the characters' high school days ("You're a fascist!") or the episode where the characters drop a water balloon on Richard Nixon's car. But the first season has some fine moments too, like anything with Ruth Dunbar (Holland Taylor) or Scolari's date with a punk rocker ("Cecily is dead -- my new name is Andrea Pus").
Or this art show, which is a pretty standard sitcom bit in terms of writing (pretentious art critics, wacky conceptual artists, blah blah blah) but which builds up to one of those Bosom Buddies lines that makes no sense out of context and is hilarious in context: "It's the flag of Japan!"