This is a Software issue with the Galaxy S III in which the compressed file isn't read properly taking a picture at a resolution less than 8 megapixels works and since the messaging app just compresses it to a lower resolution its not a really harming the quality
I had the same issue today, but had previously sent and received picture messages without problem for the twenty-some days I have been using my phone.
Interestingly enough, it would successfully compress and attach pictures that I had taken before today, but nothing today even if I took a brand new photo right then. I played with settings on the camera and still no luck, but I did not try the lower resolution. I don't always take a photo just to send in a text message so I don't think that is a sufficient fix for me, they should fix this in an update before I have to take a cut in quality.
What worked was turning the phone off and then back on. After that I was able to send even the original photo from today that first gave me the problem. I hope that I do not have to encounter this again, I was dealing with plenty of glitches and work-arounds with my [2nd warranty replacement] Droid X prior to switching to the SIII, and as I've had the SIII for less than a month, I am not pleased to encounter something like this already.
As others have stated.. rebooting will help .... temporarily. Some photos will upload while others will not. This is a very flaky and annoying glitch in the software.
Thanks so much for letting us know about the MMS error you are getting when send picture messages.
Google has been advised and they are working on a fix for this issue that will come in the form of an update.
In the interim, as suggested you can power off or change the settings for the camera pictures. Just hold on a little longer as we await the fix.
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