My (American) PS2 has been having problems for some time now, from occasionally not being able to read the memory card to not being able to read games on CD at all.  And if I want to get a PS3 at all, now is probably the time, so that I can have something potentially more dependable for playing PS1 and PS2 games while upscaling them for an inevitable HDTV (granted I'm still unemployed, so getting a job would definitely be one caveat here).

In any case, a couple questions:

1. How do PS1 games run?  Any major issues?  Is there a setting where you can turn texture smoothing on so that you don't have to do it before putting the game disc in every time like the annoying method on the PS2?
2. How do CD-ROM (blue bottom) PS2 games run?  My PS2 has never really liked these and now I can't play Ico or Sky Odyssey at all, which really really irritates me.

I can only answer your first question but PS 2 games run flawlessly.  I play mine in 1080i with full screen and it looks fantastic.  The only problem I've had is with save files getting corrupted in some Atlus/NIS RPGs.  Just make an extra save file or back up your saves to a USB flashdrive and you'll be fine.

Mine pulls the same kind of stunts... I remember a brand new God of War and WA:ACF not working on mine but working elsewhere. However, unlike you I'll probably just get another PS2 at some point - I mainly have PS1 games but they look a bit cripser on the PS2 than the PS1 and I really have no plans in going HD anytime soon. Also, minus the emotion engine is the PS3's PS1/PS2 emulation up to snuff yet?

Just an update to my post, use this to search for specific titles: http://www.us.playstation.com/Support/CompatibleStatus

LOL, nice disclaimer. What incentive is there for companies to make these patches instead of repackaging the games as a purchasable DLs?

This is the only question I can answer but I haven't had any problems with the few PS1 titles I've played on it. I've tried accessing the texture setting control from the system menu and when running a game but I can't find it for the life of me. I don't expect to get Bleemcast-level results with it so it doesn't really matter, anyway.

This is what I'm most curious about. The possibility of playing PS2 games in better resolution is exciting, but I've heard very diverse comments about it. Many people claim the difference is hardly noticeable.

Can anyone else here attest for the image quality of PS2 games?

They look great to me too.  Honestly, if I'd get a PS3, I'd get it for the whole sha-bang unless you have a PS2 with which you cannot part or have any of the PS2 Guitar Heros, since Harmonix claims the upcoming GH3 controller will not work with 2 out of 3 of them.  It disappoints me, because I really want Rock the 80s (and probably would snatch up the original) and was going to get them when I got Rock Band (I doubt the Rock Band controller will magically make those PS2 GHs compatible).  As it is, I'll just get Rock Band on 360 and will have to live without the old school GHs.

I just threw Ico in my PS3, and it loaded up just fine.  No issues at all.