I haven't really experienced any "massive" fuck-up that actually caused any harm, but here goes:
I worked at a gas station when I was 18. Had an evening shift alone when some guy starts having trouble with the carwash. I go out to help him and realize that I didn't lock the door to the station. I was gone long enough to have someone steal the contents of the cash register - the equivalent of $500 in our local currency - and about 20 packs of cigs. I was given the option of quitting voluntarily or being fired, and I chose the former so it didn't really cause too much trouble for me as I was going to move to another city in a month or so anyway.
The biggest almost fuckup, which would have had a catastrophic consequence was when I had a night shift working as a nurse and was preparing a medicine at 5 in the morning that had to be diluted in Sodium chloride. It was only thanks to my colleague who double-checked my infusion that I realized I had diluted the medicine in potassium chloride which could potentially be fatal. Nothing happened and we initiated measures against this type of confusion happening again.