The problem with 2000 was the fact that switching over to a new century, and with computers up to that point have only two digits for the year to save space, they were worried that the dates in the computers would roll back to 1900.
Because so many records and programs used the two date digit system, people were worried that the roll back would cause systems to restart or economy to crash due to bank records becoming reset, such as bank records, for example:
Let's say Mike's debt and the interest on his debt started in 1990, were the date to become reset, with computer calculated interest, if the year were to reset to 1900, his debt would become erased, and the bank might even owe him.
Of course, the media blew it way out of proportion, and eventually companies were selling "Y2K Compliant Batteries."