These ones aren't stage door, but the awkward certainly fits:
1.) I was sitting next to Kathryn Grayson at a big to-do in Las Vegas, and a woman walked up to her and asked, "Weren't you Kathryn Grayson?" I whispered, under my breath, "No, I was."
Thankfully, neither one heard me.
3.) Standing outside Birdland, having a cigarette, when Christine Ebersole and her husband walked out the front door. A girl started yelling, "OH MY GOD, THAT'S FLORENCE HENDERSON!" Not sure what was worse, her yelling, or me trying to correct her. She gave me this wide eyed look like I was speaking Dog when I said, "No, it's Christine Ebersole, she's in Grey Gardens," so I had to pull the "Richie Rich's mom..." card. At least she knew who it was, after that.
It's like writing "Norma Shearer for the win!" in a Joan Crawford biography.