just got diplomacy today, and about 45 mins into a game we realised we were totally desynced - worlds my allies owned showed as neutral on my screen, and resource asteroids did similar. Hell, i even captured some of my allies worlds, and they could see the buildings i was making in their terrirory...
It got worse as we went on - this really needs to be patched.
As for CTD's + minidumps. see here.
Thats my home forum, read the links in the post i made and it will explain the crashes you're having - the games optimised for 2GB address space (basically, ram + video ram combined) and its hitting that limit now in diplomacy. 2 minutes and you'll have a crash free game if you read the threads - note that it will only work on an x64 OS, unless you do some modifications to the OS.