The disruption is all in IT. Computers don't just magically know what time it is. They have a chip that tells them the number of microseconds since some arbitrary date (happens to be Jan 1, 1970, which means a 32bit int is gonna run out sometime around 2038 - the next "y2k" problem).
Everything else they need to be programmed to know. Every DB has its own implementation for deciding this. Every VM (including the JVM) has its own. Every OS kernel has its own. Every custom DB environment (like, say, airline reservation and tracking systems) all have their own. Every power grid system has its own.
When the rules change, these ALL need to be updated to keep up, and (this is the important bit) they kinda need to be updated in sync with each other, because each layer may be asking the previous layer what it thinks, but if someone doesn't update, say, windows XP ('cause MS won't push any patches for it), well, Java still needs to know and get it right, and so does Oracle and MySQL and PHP and any other number of things someone might be running on the XP box they can't afford to upgrade/replace (or why should they, it works just fine for what it is being used for, right?). In the airline industry, not only do the airlines need to be correct within their own systems, they need to be assured they are correct with regards to TSA's systems, and the FAA's systems, and every *separate and independent* airport's flight control tower (oh, and they all need to be correct with regards to each other as well). And that's even before we get into the issue of airline ticket purchase exchange systems, the means by which 3rd party sites like Orbitz and Priceline get their tickets - they need to be sure that they are getting the right information from every supplier of flights to their systems, or have their own means of helping the customer correct their flight reservations if they get it wrong because, say, US Airways didn't get a patch right.
So huge IT suppliers like Oracle and Microsoft and HP all need to work to keep their software correct with the changes, while not breaking the current dates before the change is actually meant to take place. Huge and small IT-dependent businesses all need to keep up with all of those patches and test their products and services on them in order to be sure they are right.
Getting it wrong could be disastrous. We got it right in 2006...but we could also have just gotten lucky. Going through that again will be painful.