Not really 25 years: many epoch problems occur before the switchover.

For example, one of the (few) serious Y2K issues affected a supermarket chain, I hear, in the mid-1990s: a shipping crate full of tins of corned beef arrived off the boat from Argentina, and was checked in to their warehouse. Following the prompts on their automated computer system, the warehouse employee put the "sell by" date of the crates of beef into the computer, and then had a forklift truck driver store them. Tinned corned beef lasts for a while, so the sell-by dates weren't until 2001 or something. The computer only used two-digit dates, so the year entered was "01".

The following morning, the computer did it's morning processing, and discovered that the corned beef that it had in stock had expired back in 1901 (which is how it interpreted the "01" it had been given the previous day). So it sent a memo to the forklift driver and had them throw out all of the corned beef. Then it realised that corned beef stocks were low, so it ordered ANOTHER shipping crate of corned beef from Argentina.

(thankfully somebody noticed before the second lot was thrown out)

No idea how much truth there is in that story, but I can imagine that it's at least partially genuine. In any case: in a similar way, the year 2038 problem will affect systems well before 2038: it might already be taking effect! Think about things like prison databases (which may record somebody's release date as being in 2039, which will be translated as ~1901, instead, or not understood at all), for example. Hopefully somebody's sanity-checking that data!