This is only a problem for hyper-accurate time keeping requirements for technologies such as GPS. As a systems engineer, we are concerned but not so much so as to be in a panic. Kerberos, for instance, has a tolerance of 10 minutes in most Windows domain environments, so one second isn’t going to be a death sentence.
Older systems (looking at you, XP!) might have trouble figuring out the change if synchronizing time from an external source, but provided they don’t sync at the exact second of the leap second, nothing will break, per se.
If you are on an older operating system (i.e. Server 2000, XP, older distros of Linux) with no more service pack support, you might expect some system abnormalities on July 1.
But GPS time doesn't adjust for leap seconds. There is a different line in the transmitted GPS time word that describes the accumulated leap seconds since GPS epoch in 1980.