One embarrassing thing is when you accidentally wet the bed during a sleepover. It's really mortifying, especially if you're older. Another is when you snore really loudly and everyone complains about it in the morning. Or if you have really bad morning breath and you end up talking too close to someone's face right after waking up.
Well, at a sleepover I went to, I had a nightmare and woke up screaming. I was so embarrassed because I woke up the whole house. Also, sometimes you might wear really old and ratty pajamas thinking no one will notice, but then someone points it out. And if you get food stuck in your teeth during a midnight snack and don't realize until the next morning, that can be quite embarrassing too. During a sleepover, you're in close quarters with others, so these little things can be really noticeable.