I've had this issue for a long time with Hangouts and it never occurred to me to try disabling Adblock. Hangouts simply refuses to download MMS messages - they'll always fail.
My solution was always to restart my S4 and then try the MMS again, and it would work. For some reason, Adblock doesn't automatically aquire root on boot and fails to start and I've got to do it manually.. That's another issue anyway.
Rather than restarting my phone this time, something made me disable adblock to try.. Sure enough, problem solved and I can replicate it by sending another MMS with adblock enabled.
So the real question is, is this an issue with adblock, an easylist entry, or Hangouts?