There must have been some things, an aweful lot of people were explicitly working on it!
I worked on a number of PCs that refused to boot during that January. In those day many PCs had to have the ROM chip replaced, no flashing. Luckily many were in sockets back then. Some people that couldn't get updates, or didn't want to bother, just set the date back 4 years, so the days of the month would be the same.
Many applications could not find data in their databases. Some had unchecked error conditions that caused GPFs. In those day a lot less machinery had computer controls. But, many did and some of it was very old, just like today.
Much effort was spent on dangerous machines and I am not aware of any that were still giving problems in the date tests, on January first.
After all, the computers and networks could have the date changed for testing, before it actually happened. Some companies built extensive isolated systems just to simulate what would happen. By the time year 2000 came everyone (well most) had been fixing for a while.
And then when we were successful, the news media said that it had all been a fraud! 8-(
But then this was often the same news people that had been encouraging people to spit on the returning soldiers from Vietnam, a few years before! So we sort of expected it...