I had a similar problem about a year ago. It's actually a pretty common problem with the PS3 Slims. Basically, the lens starts dying and can't read dual-layer Blu-Rays. The vast majority of PS3 games are on single-layer disks, so they work fine, but the vast majority of movies are on dual-layer disks, so they don't.
It could be a reader error. One thing you could try is get a lens cleaning kit and see if that helps. Also be sure the PS3 is updated with the latest firmware. If you've already done those, then the reader itself may be bad and you'd have to get it fixed.