I have played with 2 different people in Multiplayer so far in version 0.0.2.0 .  Have not been able to finish a game yet.

I have encountered this issue in both games.  Somehow the game gets stuck in between the players turns. You can move around and check stuff but the next turn wont start. Both players have the grayed out WAIT prompt on the End turn button. 

The game needs to be reloaded at this point, attempts at using console command "Turnactions" did not help.

This starts happening in late-mid game and while reloading last autosave fixes it, it seems to want to happen every other turn, which makes playing the game impractical.

I have a multiplayer save game of the problem in action. When loading this file the game resumes in the "Stuck" position.

https://dl.dropboxusercontent.com/u/43851675/MultiplayerGameIsStuck.GC3Sav

I might also report another issue: After reloading the last autosave after the bug,  my Planet Production wheel settings were all reset to the middle position.

I noticed this while the other player was hosting. Cannot give more information at this point, but each reload produced this.