When you know you messed up, does it show on your face? Does everyone know? 
The answer is yes.

Your cheeks turn a shade rosier than before, your eyes form a glossy coat, and you look around as if the walls around you would give you some sort of answer.
As you look to the left, their eyes move in that direction too. They look though they won't be able to know exactly what you are looking at.

I mess up all the time. I stutter over my words and leave myself looking like a complete idiot. One thing that I don't do though, is judge others for making mistakes. It makes me nervous when a peer messes up. I don't want them to feel obligated to apologize. We all mess up. We are all imperfect. We are all human.