I don't see any reason to panic. What I fear is that some trivial little thing may go wrong, like a random ATM blinking out of order, and somebody doing the Chicken Little thing and blaming it on Y2K. It will never dawn on this guy that ATMs have gone out of order before Y2K. Or maybe a drunk plows into a light pole and a couple of blocks lose their power. This would be all that is needed to cause a panic.
For my part, I will deposit my check, like I always do, then spend the New Year's Eve at a party. Maybe all the paranoid nuts will have run to the hills and I won't have to worry about traffic.