Judy Garland's character's name, Ginger Gray, is a tribute to Ginger Rogers, who played the part on Broadway where the character was named Molly Gray. Rogers wrote that one night on stage, her co-star Allen Kearns accidentally said, "Ginger, I love you" instead of "Molly". The mistake got such a huge laugh from the audience that they decided to continue to do that in subsequent performances, pretending it was a mistake.
The musical play opened on Broadway on 10/14/30 and had 272 performances. The leads were played by Ginger Rogers and Allen Kearns, but the cast also included Ethel Merman in her first Broadway production. She was featured in the "I Got Rhythm" number. "Girl Crazy" was later revised as a new musical, "Crazy For You," which opened on Broadway in 1992, starring Harry Groener and Jodi Benson. It won the 1992 Tony Award for Best Musical and ran for 1,622 performances.
After Busby Berkeley finished directing the finale ("I Got Rhythm" number, which was filmed first), he was fired by producer Arthur Freed and replaced by Norman Taurog. The reasons vary: modern sources say he was way over budget and behind schedule. Freed himself claimed it was because of a personality clash with Judy Garland, who requested his dismissal.
The film came in at $1.4 million--over budget by $323,000, with at least a third of that amount attributable to Busby Berkeley's removal and subsequent shutdown of production. The film went to on to be one of the most profitable of the Judy Garland / Mickey Rooney musicals, taking a total $3,770,000 on first release.
One of the students from the college discussing the telegram sent by Daniel Churchill Jr. (Mickey Rooney) is Peter Lawford (at about 53 min).