I also have the Samsung Galaxy S3 for AT&T and the only APN settings that work for me are the following:
MMS Proxy: 184.108.40.206
MMS Port: 80
MMS works fine, both receiving and sending. The only problem I am having is that the internet is coming up really slow. Whenever I try opening an app, it takes quite some time before it actually loads. My boyfriend has an HTC Vivid and is also having the problem with not being able to receive mms. We are definitely thinking of switching services if this issue isn't resolved.