Not embarrassing but: the summer after my buddy and I studied abroad in Denmark we traveled to Paris and creepy guys kept trying to hit on us (cluing in that we were Americans and thus must be Loose Women). So we'd insist, in broken Danish-accented French, that we were from Jutland didn't speak English. Totally befuddled them! :)

As for embarrassing: on that same trip, in Madrid, after a long night at some club, it was my turn to buy the next round of drinks. I wove my way up to the bartender and asked him sweetly, "Dos cabezas, por favor." (cabeza/cerveza... it's an easy mistake after your 4th one!!!)