I know this isn't the ideal method for reporting, but understand I have been busy and I would like to report in what limited fashion I can today. This is a listing of bugs encountered over numerous gaming attempts. All of which were multiplayer ranging from 2-4 players.
The 1st bug that was noticed was ideology events were not being triggered by any players actions. This appears to be a constant for all multiplayer attempts.
Diplomacy tech trading appears to list researches that a player may not have. If the initiating player offers a tech they do not actually poses it has caused the other player to crash right after the trade. In addition to that it will often list the diplomatic recipients current research on their list of tradeables. This has been repeatable for all multiplayer attempts.
Multiplayer stability has a long way to go and led to us attempting to restore games frequently. Not a complaint, I understand the work it takes and know it will get there. With the current 5.3 opt in beta any attempt to reload a save for multiplayer leads to players getting incorrect lobby information. EX. Player 2 enters lobby and is listed (to him) as player 1's race. This compounds when you add 3 or 4 players. As the host I observed it displaying incorrectly only once and I have a picture to demonstrate the errors.
In the posted picture below you can see my lobby screen after loading a save. Several race names appear to be missing, one of the players names is listed under an AI (Player not currently in lobby), and the AI teams appear to be jumbled up.
I hope this is helpful, and if anyone were to have questions please feel free, I will try to get to them later tonight if possible.