Reuters has just posted an article
saying the Japanese PS3 has problems running roughly 200 games from the PlayStation and PlayStation 2 catalogs. Their source is the Japanese Sankei Shimbun newspaper, and a bad Google translation of the original article
does indeed say a "portion of the game software of PS and PS2 of the expectation which is compatibility not to operate just."
The short, translated article doesn't detail which of the thousands of PS and PS2 games aren't working or how many were tested, but it does quote someone from Sony as saying ""when system renewal of the substance and you improve with the software individual correction software, there is," which we can only assume means that future system updates will fix this problem (we've signed up for Japanese classes).
For reference, our backward compatibility tests with various PlayStation and PlayStation 2 software on the U.S. retail console turned up no problems. Then again, we only tested a handful of discs as we don't have the time or resources to test every PlayStation game ever made. If we hear about any similar problems with the American version of the system, you'll be the first to know.
[Update: fixed link to the Japanese translation.]