Visible crew/equipment: During the Broadway Melody, the shadow of the hanging boom mic becomes visible. This happens during the sequence filmed in the large sound stage. Kelly is dancing with a woman with a long fabric flowing behind her. The shadow is on the right side.
Suggested correction: I can see no shadow at any point in this scene. Could you provide a time stamp or screen capture? Besides, there is no spoken dialog or even any natural sound in the scene. Why would they be using a boom mike?
It's on the right, center side of the screen when the lady with the long flowing dress is further away and the shot cranes up. This is a musical number, Kelly is singing. They would still use a microphone.
Are you talking about the fantasy sequence between Kelley and Cyd Charisse? If you mean the faint shadow at 1:25:18, that is a shadow from the flowing cloth. And no, they would not be using a microphone. 1) There is no singing in that sequence. 2) In musicals at the time, all singing was pre-recorded and the actors lip-synced to a playback on stage.