Poking around on a few different sites, I found you can, to a degree, protect yourself from most, if not all problems. You change some settings in either Hangouts, or possibly your text messaging app. Under settings, you can disable auto retrieve MMS. This can be done in Google Messenger as well.
I updated my S3 using the Stagefright patch and my phone is hanging on the Samsung Splash screen. Please provide feedback if others are experiencing this. I found someone on the Sprint Community Board that experienced the same problem.
Sprint's S3 sofwtare updates page (see lame substitute for a link below) finally shows the Stage Fright patch. Of course I got the mystery update notification well before they posted anything and got to wonder about it for a week. Now that I know what it is, I'm still going to wait a few days to see if problems like askskeeter's are one-offs or widespread.
Well I had to reinstall the previous Sprint version using Odin Flash. Stagefright really messed up my phone. Several others have reported the same problems in the Sprint Community Board.
If you're running a custom rom, just copy these update files that were copied from an already updated S3. Paste into system/lib/ all 27 files and change permissions to rw-r-r- (0644), then reboot. All should be good. Worked for me on my other S3. Be Sure to do a nandroid backup first!