It wasn't so much the Millenium that was the problem but the year 2000 itself. Older computer programs, to save precious disk space, used two-digit years for calculations, etc. Since numbers could be 'packed' to use less bytes than characters, years were stored as decimal numbers. Financial institutions used the last two digits of the year as part of their 'period' concept (ie 9901 would be the first period of 1999; 0001 would be the first period of 2000). Since leading zeros usually get truncated, the period 0001 would really be 1.
The reason that nothing major happened was that programmers recognized the problem in advance and corporations put out big bucks to either fix or replace systems. Nothing happened because the programmers did a good job, though a very unrecognized good job. There were a few things, though: In New Hampshire, all year 2000 automobiles purchased were listed on the titles as 'horseless carriages' because the system thought they were made before 1901. But as I said: the programmers did their job; quietly and effectively, so that all the doomsayers looked like idiots when 2001 roled around.