While not really a Greek ritual, here's one memorable goof I did during a Masonic initiation ritual:
I was the Senior Steward at an Entered Apprentice (first) degree over at the lodge I belog to (Will Rogers #53, Claremore, Oklahoma), and at a certain point in the ritual where the candidate for initiation is presented at the door to the lodge room there is a few lines the Senior Steward recites when the door is answered by the Senior Deacon. I reply with the prescribed words for my part, absolutely letter perfect... except it was Texas Masonic ritual instead of Oklahoma. (They're similar, but different.)
And you'd never guess who happened to be attending the ceremony that evening -- two past Oklahoma Grand Masters who were accomplished masters of Oklahoma Masonic ritual. The brethren of my lodge never let me live it down for the rest of the time I was in Oklahoma!
