Interestingly Y2K is not over. In Norway for example the national insurance number has year as a two digit string. A small number of people every year find themselves in a position where the state considers them as eligible to for instance re-attend kindergarten... At some point in the 21st century duplicate numbers may start being issued.
There will be long tail of repercussions to using two digit years for most of the rest of the century.
There's also the 2038 problem [1] although it apparently is mostly an issue with embedded systems. It's not clear that it's a particularly widespread problem but that's mostly just based on the fact that there doesn't seem to be much discussion about it.
There's also the Y2036 problem which is part of Y2038, and other issues in 2028, 2040, 2042, 2048, 2050, 2079, 2080, 2100, 2106, 2108, 2137, 2262, 10,000, 32,768 and 65,536 - although I'm sure by the time we reach the latter end of the list we'll have replaced the affected systems ;)
There will be long tail of repercussions to using two digit years for most of the rest of the century.