The second that was added before July 1st was taken into consideration by NTP and thus the date 30th June 23:59:60 was created.
Important sites like Gawker, Reddit, Mozilla and others experienced a short downtime caused by what seemed to be technical problems. After the system administrators fixed the problems some companies publicly posted information in regards to their problems. The site downtime was caused by running operations that crashed when the leap second happened because of the time synchronization.
Only Google and few other companies anticipated that the leap second could potentially cause problems and thus prepared for this. Web servers were not the only computers that experienced problems. According to many online publications companies worldwide complained that they had issues with Linux servers.