This link in Network World documents impacts caused by adding an additional second to the day and systems using the Network Time Protocol going out sync.  However, this year more advanced preparation kept vast majority of networks running smoothly throughout the transition.

http://www.networkworld.com/article/2942994/leap-second-causes-internet-hiccup-particularly-in-brazil.html

The addition of a leap second to world clocks on Wednesday caused some networks to crash although most quickly recovered.  Some 2,000 networks stopped working just after midnight Coordinated Universal Time (UTC), said Doug Madory, director of Internet analysis with Dyn, a company studies global Internet traffic flows.

Nearly 50 percent of those networks were in Brazil, which may indicate that ISPs use a common type of router that may not have been prepared for the leap second, he said.  Most of the networks quickly recovered, which may have required just a reboot of a router, Madory said.

The Internet’s global routing table, a distributed database of networks and how they connect, contains more than 500,000 networks, so the problems affected less than a half a percent, Madory said. The last leap second, added in 2012, caused problems for Linux systems such as slowdowns or CPU freezes. This time around, however, many companies looked to avoid issues with better preparation.