Dudley Moore was said to have based his performance partly on Peter Cook, whose excessive drinking had soured his and Moore's comedic partnership in the 1970s.
At one point during the production, Liza Minnelli was supposed to board a bus in front of Bergdorf's on Fifth Avenue. When a real bus came along, she boarded it thinking it was the "movie bus". Not until she was halfway down the block did she realize her blunder when she looked back and saw the whole crew cracking up.
During the famous moose scene, Dudley Moore kept ad-libbing so much that Stephen Elliott got enraged at having to do so many takes, he said, "Will you forget about the moose, for now". You can tell by Moore's reaction that it wasn't in the script. Director Steve Gordon halted filming and begged Moore to play the scene straight. That's why Elliot's tone changed so suddenly.
The movie's song, "Arthur's Theme (Best That You Can Do)", was co-written by Christopher Cross, Burt Bacharach, Carole Bayer Sager, and Peter Allen, who was Liza Minnelli's ex-husband. Allen's only contribution to the song was its famous chorus lyric ("When you get caught between the moon and New York City, the best that you can do is fall in love.") He came up with this line while sitting on an airplane that was stuck in a holding pattern over New York City at night, waiting to land at John F. Kennedy International Airport. Despite his minimal contribution, the other three songwriters insisted that Allen receive a songwriting credit. He ended up winning an Academy Award for Best Song, just for this small, but very important contribution.
Sir John Gielgud turned down the role of Hobson several times, finally accepting it only because the salary he was offered was too good to pass up.