Someone has re-uploaded clips from the D.A. Pennebaker documentary on the recording of Company, still the best documentary on how an original cast recording is made. (Most of these things are very pre-packaged and phony -- basically, promos for the recording and the show -- but Pennebaker actually got to convey how it feels for tired performers to do a long, exhausting recording session where they have to create "definitive" performances of the songs.)
One thing I always like in this documentary, a sign of the times, is seeing the huge contrasts in fashion: everybody's wearing different styles of clothing because this is 1970 and nobody knew how they were supposed to dress. You've got everything from miniskirts and high collars to jackets and ties. The first person we see is Fred Plaut, CBS/Columbia's chief recording engineer, a German who fled the Nazis in 1940; he was 62 years old at this point and had worked on almost every Columbia Broadway or classical recording made in New York. He's wearing a tie and has a blank expression on his face, the epitome of the engineer who is concentrating on technical problems and is not there to pass judgment on the music or the young whippersnappers in his studio:
Plaut is also seen smoking a pipe in the studio in the "You Could Drive a Person Crazy" sequence (maybe my favorite sequence in the documentary, though Elaine Stritch's struggles with "The Ladies Who Lunch" are the most spectacular). Couldn't get away with that in a recording studio today.
One thing to add about Company is that it gives a disproportionate number of the big musical numbers to three very minor characters: Robert's three girlfriends, played by Susan Browning (April), Pamela Myers (Marta) and Donna McKechnie (Kathy). Even though they function in the show mostly as illustrations of Robert's inability to commit, they carry a lot of the songs and dances: not only do they get "Crazy," but Browning got the funniest duet ("Barcelona"), Myers got the best solo song ("Another Hundred People") and McKechnie got a huge solo dance number ("Tick Tock," with music by David Shire based on themes from the show, which is often cut in revivals).
The reason for this was partly that Robert's friends were mostly cast with actors who could sort of sing and dance, as opposed to professional singers and dancers; that meant that the three young women were around for anything that required a bigger voice or first-rate dance skills. But it was also because Company was the first show in a long time to revive the idea of giving big numbers to minor characters, and generally assigning numbers in ways you wouldn't expect.
Rodgers and Hammerstein had already tried this in Allegro (1947), where the main character doesn't sing all that much, the biggest ballad ("So Far") goes to a character who never appears in the show again after the song finishes, another big ballad ("A Fellow Needs a Girl") is not for the hero but for his parents, and many of the numbers provide commentaries on the action or the themes of the show rather than directly moving the plot along. But in general, most "integrated," artistically ambitious musicals gave the bulk of the musical numbers to the main characters and placed numbers at big emotional moments in the story. Company went back to the idea that Rodgers and Hammerstein had abandoned after Allegro, that a show could actually be more surprising and interesting if the songs occur at unanticipated moments, from unexpected characters. It still doesn't happen very often, though (even Prince and Sondheim didn't stick with this idea all that much).