I work at a fairly large international outfit, with data feeds coming and going to the far ends of the Earth. Everything we do is time-sensitive. Processing messages that depend on prior messages already being processed means we can't gracefully handle things coming in out of order.
We spent lots of time and money studying this problem, hired a high-priced consulting outfit to advise us and spun up lots of projects to mitigate the "risk" of the leap second. There were far too many meetings and conference calls with vendors, VARS and other people that wanted us to pay them for their time. What was determined was that we couldn't guarantee that nothing would crash or (gasp!) messages might be discarded or processed incorrectly, which was a risk we weren't willing to take. We run a full gamut of OSes, from HP/UX, Solaris, Linux, z/TPF, z/OS, DB2 etc etc.. You get the idea. Too many variables and too many systems to update and test with the limited funds and limited timeframe given.
In the end, we avoided the problem by shutting down all (and I do mean ALL) processing and flushing all the transactional systems to disk and suspending EVERYTHING from a minute before until a minute after the leap second. (Was that two minutes or two minutes PLUS one second? Clock math has always eluded me.) Shutting down all these interconnected systems in the correct order was a precision dance that, in the end, we didn't perform very well. Messages did end up being discarded. At precisely :20 seconds after the leap second, we began syncing all our systems with our internal NTP server and then at precisely one minute after, we slowly started everything back up. There were some systems that required a restart. We manually reprocessed those earlier discarded messages just as fast as our little fingers could type. In all it took us about 15 minutes to get everything spun back up, and all that time is getting charged to our SLA, which affects ALL our evaluations and year-end bonuses.
Lots of work was done, overtime was paid and buckets of money were given to lots of high-priced consultants and I personally will take a hit to my paycheck, all over ONE GODDAMNED SECOND.
Let's not do that again, okay?