Y2K mostly ended up being a non-issue because all of the "bugs" were taken care of ahead of time. A lot of the COBOL code that banks used would have definitely been a big issue since for the most part it only supported 2 digit dates. Now, I'm not exactly sure what would have happened if banks suddenly thought it was 1900 again but probably nothing good. There were a few years leading up to Y2K that it was a great time to be a retired COBOL programmer looking for some extra money. It was a non-issue for PCs (even if it was a bug that wasn't patched it wouldn't have been that big of a deal for most people). Not sure how other industries would have been affected but I don't think planes would have fallen out of the sky or anything.
Taking a look at songs released in the Y2K era, it's hard to believe some of them are 25 years old...