This is one of those WWII era musicals where a studio assembles all their top talent for an all-star extravaganza. The stars' appearances are incorporated via a very thin plot. The plot doesn't matter, because the real point in watching this film is to see the musical talent.
This film stars Kathryn Grayson who is the daughter of military colonel John Boles and Mary Astor. Grayson is a singer who is performing onstage with Jose Iturbi. Grayson decides to put her musical career on hold in order to entertain the troops on her father's base. One of her father's new recruits is acrobat Gene Kelly, who is drafted into the Army, but would rather be in the Air Force. Kelly and Grayson end up falling in love (of course). Things are complicated when Astor wants to take Grayson back home because she doesn't want Grayson falling in love with a soldier. Astor tells her that being the wife of a soldier is undesirable because the army will always be a priority. There is also another subplot where Grayson tries to get her parents back together. The highlight of the first half, IMHO, is Gene Kelly's "Let Me Call You Sweetheart" dance with a broom.
However, all of that plot is meaningless, because the second half of the film is where all the action is. Mickey Rooney appears as himself. He emcees the show and also provides some impressions along the way. The best performances in the second half are Eleanor Powell, Lena Horne and Judy Garland's. Lucille Ball, Ann Sothern and Marcia Hunt appear in a skit with Frank Morgan, and Donna Reed and Margaret O'Brien appear in a routine with Red Skelton. Virginia O'Brien does another of her awful deadpan routines with Gloria de Haven and June Allyson providing support. Gene Kelly's stunt double performs a trapeze act. Kathryn Grayson come out to sing another song while, almost literally, "thousands cheer" - the soldiers that is.
Thousands Cheer is an average film viewed from today, although it is fun to watch for Kelly, Garland, Powell, and Horne. As little as they gave Kelly to do here, you can tell MGM just didn't know what to do with the fellow yet After all he had only been on the MGM lot for about a year. However, they did give him some great comic bits.
I guess you have to view this one from the wartime perspective of when the world was a canteen and morale boosting on the home front was the order of the day.