Judy Garland is said to have been at the height of her drug addiction throughout filming, resulting in her weight changes, mood-swings, and unexplained illnesses. It was due to this behavior that MGM fired her after filming completed.
The number "Heavenly Music" was originally a trio with Gene Kelly, Phil Silvers and Judy Garland. Garland didn't show up to work the day of shooting and they filmed the scene without her. In the scene immediately following (but shot out of sequence) Kelly, Silvers and Garland are all in the "hayseed" costumes.
The number "Get Happy" was filmed several months after the rest of the film. During that time, Judy Garland lost considerable weight, which led to a longtime legend that the number was shot for a different film. In fact, Garland had worn the exact same costume in a deleted musical number from Easter Parade (1948), which also contributed to the false legend.