I can think of many things I have done that are daft, but they're scarcely unique.
For example, I think of being so obsessed about The Beatles at school that I managed to write writ an embarrassing letter based on that obsession for my mock O level English, only to find out afterwards that on a second sheet of paper were the instructions as to what the letter should be about.
Now that may qualify for the list but I think of it just as "idiot girl forgot to read the instructions for her exam and made a fool of herself". Unique to the history of humanity? I think not.
I could also suggest waiting outside the Royal Concert Hall in Nottingham to meet Lloyd Cole after a concert only to find I had no paper for him to autograph except a letter from my bank charging me for an unauthorized overdraft. Though I was chuffed to bits to meet him (tall, handsome, floppy hair - sigh) within a short amount of time I had managed to lose the letter and the autograph in a fit of bank paperwork filing and chucking.
Again, "idiot girl manages to get autograph on unexpected surface only to lose it because it is on an unexpected surface". I say again, not unique.
Now you would also spot that in neither instance is the act "cool" (a requirement of the original post). Well that would be easily explained by my complete lack of coolness! I don't do cool! I do geekiness (an insane level of cataloguing books, photocopies, records, CDs, tapes, films etc etc nigh unheard of for a girl); I do clutziness (you want stories of my falling over in stupid places? t-shirts galore for that act); I do embarrassing acts of inappropriate mistakes (more examples than you could ever list).
What I don't do is cool.
Maybe I just need to get another perspective...