My friend and I started a new MP game, using V 0.92. We played 42 turns, or about 3.5 hours today. We played over my LAN at my house.
As there were no AI opponents in this version, we played the default Arena game.
I started the new MP game, but then my friend could not see my new MP game on my LAN. There was a Queries Lobby Failure message. This happened several times. I started a new MP game and he eventually he managed to see my game in lobby and join it.
In the course of the first hour of play, we had no issues, then the game started to freeze at the end of my - the Terran Alliance - turn. The turn arrow was shown at the bottom right, but the game was frozen. I had to use Ctl-Alt-Del to exit the game. This happened about 6 turns in a row - always at the end of my turn. I would then re-load the auto-save, get in maybe one more turn, then the same freeze would happen.
In one case, where I had reloaded the saved autosave game, my friend got the Queries Lobby Failure error, when he attempted to join my saved MP game. After several re-loads and attempts to join, he finally managed to see my game in the lobby and join it.
Eventually this behaviour stopped and we were able to play the last 1.5 hours of our session with no freezes. We did no diplomacy as we were at war, due to the Arena game rules.