Probably the biggest let-down from not having raw images is that in substituting processed jpg images you're denied the opportunity to start from scratch with a PP program that can usually get better results. In camera noise reduction, for instance, can usually be bettered by Neat Image or similar programs. Blown highlights can often be recovered from a raw image but they are lost once converted to jpg, although shadow detail can more easily be recovered.
So there IS some benefit from raw, even with a compact camera, but in practice it's a PITA because compacts take ages to write the image to media, the images are huge, and you have to mess around with them for ages to get a print. People expect to do this with a DSLR but it's not what a compact is all about.
If you think about what you're shooting, try to avoid high ISOs with their inherent high noise, underexpose by 1/3 stop in high contrast lighting to limit blown highlights, then you can mostly compensate for jpg image shortcomings. And to be fair to the S3, unlike other manufacturers, Canon were reasonably easy on the in-camera noise reduction that didn't blast away all the detail in high ISO shots, meaning that Neat Image can do quite a good job of cleaning it up and still retain some detail.