I've made plenty of embarrassing mistakes speaking Japanese, but I think that my most embarrassing mistake was this one that happened when my 2 older children were in elementary school.
It was the early evening when my phone rang. My children and I were there together. I answered, and it was a "phone tree" call (連絡網) about my children's school. This kind of phone call always made me so nervous. I knew that I should try to use polite Japanese with the other mothers from my children's classes. And I also always panicked because I felt great pressure to understand the message correctly so I could tell the next person.
The woman on the other end of the line gave me the message. I tried to write everything she said on a piece of paper, clearly enough so that I could read it to the person that I had to call next.
At the end of the message, I suddenly realized that I had missed the beginning of the message--important information! Which of my children's classes did this message come from, my daughter's or my son's?
I decided quickly that I would ask her as politely as I could to repeat her name to me. I knew that it wasn't polite to ask, "あなただれ？” What was the polite way to ask that question?
I asked...
"何様でしょうか？"
My children immediately began laughing very loudly, and I knew I must have made a mistake. 
Luckily, the mother on the other end of the line had a sense of humor. She laughed and said, "Don't worry!" as I apologized.
Please tell me that you have done embarrassing things in your life! It's not only me, is it?