If someone tries to send your iPhone an MMS message, you can't actually get it. Instead, you get a stupid text message with a link to a AT&T website that uses a special id code AND password. AT&T is not smart enough to embed any of that information into the URL, and the iPhone doesn't support cut and paste - which means the link is pretty much useless.
However, even if you have computer handy, apparently you - as I did- can just get the above message and no picture whatsoever. The ID and password are correct, because if they aren't you get a different error message. AT&T is just incapable of displaying the image even in this hobbled, half-assed manner.
For a device which prides itself on user friendliness, this is about as user unfriendly as you can get. My old Windows smartphone handled this stuff like a champ. I've complained about this before, but this is the first time I've had both the phone and the website fail me.