On New Year's Eve 1999, when we flip from 31/12/99 to 01/01/00, many computers won't know what Year 00 is and will assume either it's 1900 or nil-input.
This is an important issue that must be examined. Any company, organization, or government that doesn't take the time to look at how their systems will operate in the Year 00 is inviting disaster.
But ... most companies, organizations, and governments are doing or have already done so. The only reason to panic or worry would be if no one was doing anything about it. The issue does indeed exist; it's just not as gigantic a problem as it has been inflated to be.

