A surprising amount of software behaves badly if there aren't 60 seconds in every minute. There were a number of unexpected software glitches when the 2016 leap second occurred. At least one large-ish service shut down for an hour before that one, just in case. It's enough of a problem that Google (and others) don't implement it as a single second, but "smear" it out over 24 hours with their time servers running very slightly fast or slow (depending on whether a second is being dropped or added).

ThTh1: Nothing about leap seconds? Those are turning out to be problematic for soft real-time applications, since they occur irregularly and can be either positive or negative in sign.