Meanwhile, happy new year: classic Mac systems prior to Mac OS 9 are now hit by the Y2K20 bug, where you cannot manually use the Date and Time Control Panel to set the clock to years beyond 2019 (see also Apple Technote TN1049). This does not affect any version of MacOS 9 nor Classic on OS X, and even affected versions of the classic MacOS can still maintain the correct date until February 6, 2040 at 6:28:15 AM when the unsigned 32-bit date overflows. If you need to set the date on an older system or 68K Mac, you can either use a CDEV like Network Time, which lets you sync to a network time source or a local server if you have one configured (as I do), or you can use Rob Braun's SetDate, which allows you to manually enter a date or time through the entire supported range (and even supports System 6).
One other note is that all HFS+ volumes regardless of operating system version have the same year 2040 limit on dates -- that includes Intel Macs using HFS+ filesystems. You have 20 years to think about how you want to fix this (during which you should replace the PRAM batteries in your classic Macs, too).