First time I saw it in anger? 1991(!) 99 months in Duration field is considered permanent (don't ask, just remember the monkeys, bananas and fire hose). Purge process calculated duration in months between start date and now, if greater than Duration, it goes. New Purge, written by ex-colleague calculated the end date as start date + duration......(!) I rang him up at his new company to congratulate him on being the first person to exploit the Y2K bug.
Daftest moment? With Old Father Time breathing down our necks we're in a race to roll out the compliant versions before, er, Y2K. A business unit stalls the entire process by stating that their methodology required a Feasibility Study before any changes and there wasn't one for the new software versions so they wouldn't put it in. We countered with the fact that the 1st of January 2000 wasn't going to move or change so we had had to do it, feasible or not, so we weren't going to waste valuable time on meaningless bollocks. As "get stuffed" trumps wankword bullshit, they fell into line.
Most visible cockup? The US Naval Observatory clock on the web proudly showing the date as 1/1/100. Hooray for ctime. This really cheered up the manager of one of our development teams, who'd been upset to find all their report headers doing the same thing and had asked me to find out why.