The PS3's backwards compatibility program was hyped as being perfect, and while it fell just shy of that, PSXE's testing reported no problems with any titles tested. However, those 200 PS1 and PS2 games that don't work on the PS3 are still out there somewhere, and Sony has recognized the issue. They expect to fix the problems "soon" with a downloadable update.
But in the meantime, they've put up an online database for users to search their games and find out if some may experience problems when playing on the PS3. Most of the glitches are extremely minor; e.g., a "small black box appears around the cursor during the first battle in the Mako Reactor" in Final Fantasy VII (which we didn't notice, by the way). Just about all the problems tend to revolve around these tiny graphical imperfections or audio skips, even though some issues are obviously more severe.
So if you want the exact status of the game in question, check here and cross your fingers. Based on our experiences, though, you should be fine…provided you don't have the bad luck of owning one of those games that has no sound at all.