After three hour+ calls to Net10 Tech Support and over a hundred hours of research and troubleshooting online, I figured out why I couldn't receive MMS and fixed it for ten bucks.
It turns out that my AT&T micro-SIM was faulty, and that no amount of troubleshooting would fix it. I asked Net10 on the phone if the issue could be a bad SIM, and the rep said "No. If it were a faulty SIM, nothing would work".
After thinking it might be the issue, myself, and finding a post here where someone said a new SIM got them working, I went to Dollar General and picked up a BYOP SIM kit (which comes with T-Mo and both micro and standard sized AT&T SIMs), transferred my existing Net10 number to it, and about fifteen minutes after the new SIM started working, I was able to receive MMS just fine.
If you can send and receive SMS, and can send but not receive MMS, do the following to check for a faulty SIM:
In your Messaging app, go into Settings and uncheck "Auto-Retrieve MMS"
Send yourself a picture mesage larger than 50kb
Wait for the text to come back
If the attachment waiting to be downloaded is 32kb or less, you have a faulty SIM. Go buy a new SIM kit and transfer your number.
While this issue happened with my Nexus 4, it's completely device independent, so if you're able to send but not receive mms, and ESPECIALLY if you're on AT&T, then try this.
I pulled my hair out for a week trying to fix this. I wrote this post in hopes of saving the rest of you the trouble. If there's any wisdom on these forums, this will get stickied to the top of every GSM forum here.