At least on Cisco systems, you can add a leap second [1], and at least on my network the tolerance is set at 5 minutes. So network time should still be working. For clients that might not know how to deal with a leap second but still poll network time, I only see issues in the rare case that the client polls the server at exactly 23:59:60. In that situation, they might poll back again to grab a new time thinking it's wrong.

Of course there will always be outliers and poorly coded applications that rely on time, but at least it's not a Y2K style situation.

[1] http://www.cisco.com/en/US/tech/tk869/tk769/technologies_whi...