My rebug PS3 slim has many PS2 iso's on it and they run fine. A good chunk of my favorite PS2 games were rolled over as HD classics for the PS3 or got official PS2 Classic releases, but for those that were never re-released on the PS3 I've made iso's and only recall a couple of them not working (Hulk Ultimate Destruction had some glitching in the backgrounds, and I'm sure there were a couple of other games that I couldn't play). For those that didn't play perfectly I just removed them, but I still have a boatload of them on the PS3 and they work great.
My PS3 slim is probably my all-time favorite system as it has my huge library of PS1, PS2, and PS3 games (1tb internal drive and 2tb external). The Wii-U is a close 2nd (having all my Wii, Gamecube, and Wii-U games on it).