It didn’t cause major problems because a lot of IT folks spent a lot of time to make sure everything was patched up and tested.
Where I worked, every PC, (mostly W95), had the BIOS tested and fixed, if needed. Older OSen, like Netware 3.11, 4.10, and 4.11 were updated and tested. Remember synthetic time on Netware when you rolled the date into the future, and then rolled it back, (NDS) ?
Accounting software had to be tested also, dates are pretty important in that regard.
It was a big deal.
Many good replies concerning the end of civilization, but with all due respect I think it will probably end as depicted in the following video.
Mahalo
http://www.youtube.com/watch?v=JIgIWL-qElM