I my case there is no button - I can't even scroll down. But I also don't get any error message, especially not "domain error 912".
If I try to open the .mov file the screen shows the movie-progressbar (where you can normally scroll through the video) for half a second and then the screen goes gray. In the middle of the gray screen I can see the file name and the text "QuickTime-Film" (german version) and the file size. Underneath is a "play-button" (with no reaction if I click on it) and the buttons for forwarding the movie and the button for airplay. No "Download full message"-button.
Seems that we are having different problems with more or less the same result. Again, it only seems to happen with mail which was sent through MS Exchange and it started with IOS 7.1. Therefore I don't think that we can fix it but I hope that someone from Apple is "listening".
My fault! I misunderstood your posting - I was looking for a "download full message"-Button on the screen AFTER clicking on the movie icon. But you meant the mail itself - and there I found it. Thanx! That also explains why small mail went through without problems but larger didn't.