Everything has been patched thoroughly at this point. You may find some PS2 games that have problems but from what I have seen no PS1 games are affected. This is just from what I have seen remember.

I rarely play PS1 games on my PS3 because I don't have a memory card adapter yet so I just play them on my PS2 (yes I still have it out). I gave IX and VII a whirl a while back and they played fine. And to be honest they're the only ones you really need to be playing.