The backwards compatibility of the PS3 has been a gigantic plus thus far, despite some minor sound issues and a few more obscure PS1 and PS2 titles not functioning properly. However, until today, PS2 games that used the hard drive wouldn't work at all…although it may not be 100% fixed.
The latest PS3 firmware patch, version 1.31 update, supposedly allows both Final Fantasy XI and the Japanese-only Nobunaga's Ambition Online to work on the PS3. However, those were the only two titles Sony specifically mentioned, so we don't yet know if this update affects other hard drive-oriented PS2 games.
A minor security patch is also included, along with a few more options regarding the user's control over how the web browser displays text. Just bear in mind these details aren't "official," even though we just downloaded v1.31 a few hours ago without a problem…but we don't have either of those online games to test right now.
As for those other small issues plaguing some of the PS2 and PS1 games when played on the PS3, Sony is apparently working on clearing all that up with a major firmware update scheduled to arrive in March.