I was having a very similar problem and thanks to this forum stumbled on a solution. I'm not familiar enough with the S3 to know about connecting to a computer, but maybe this will help instead. It's a very simple solution so you may have already tried it. However being a complete novice on the S3, this issue stumped me (and several other novices) for quite a while.
So... 1. After saving the the photo from the mms, open your gallery. 2. Once there, use the back button (to the right of the home button) to navigate to the last (or earliest) screen in your gallery before returning to your phone's home screen (ie, the screen in gallery where if you pressed back once more, you would go to one of your home pages). 3. Once at that last gallery page, press your options button (to the left of your home button) and select 'View by'. 4. This should open a box giving you several choices of where you want to view pictures from. Select 'All content' or 'Content in device'. 5. This should bring up your pictures if they did save to your phone.
I realize step 2 is a bit confusing. Basically I'm just trying to navigate you to a page where you'll be able to see the 'View by' when you hit the options button. I found that not all pages offer that. Also, for me the phone was automatically set to 'Content in Picasa' and thus only showed those pictures and not any from my phone. Again, I'm very much a novice and realize there may be an easier way to do what I did, but at least it worked for me. I sincerely hope this helps.