The "fat" PS3s were more prone to issues than the slims without question, but never were "major" like the unfortunate folks who RROD'd with their 360s.
I have a launch unit at 60 gigs that YLODed on me (fixed for free by Sony), and have two more 80 gig fats from year 2 (one for upstairs and one for my brother in law) where neither ever shown issue.
Statistically the PS3 has been a tank from a failure rate standpoint, fat or slim. (As are the newer / cooler 360s if my info is correct.) Good time to pick up a used "newer" model for anyone with either system if it's from the last 2 years, imho....