I saw a tour of THE SOUND OF MUSIC with Marie Osmond as Maria, and during the title song, she's twirling around, and her wig falls off as she's dancing/singing. I was sitting far back, and it took me a second to realize what happened. I thought for some reason she had a dog on stage...but it was her wig. Then I noticed her wig cap. She made no attempt to pick up the wig during the number. I believe she just kicked it off stage at the end of the scene.
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Although this isn't really a noticeable mishap, I saw MISS SAIGON on tour once and was sitting in the front row. Kim draws a gun on Thuy and then kills him. She over-gesticulated after shooting him and her gun went flying across the stage floor and skidded onto the orchestra pit cover, and landed at my feet! At intermission a crew member discreetly went through the pass-thru door and I gave him his prop.
<---- You can see the crazy in her eyes. ;-)