The game approaches civ5-level stability with a good host: maybe a crash requiring a reload every 1-2 hours. This is annoying but workable if everyone has the host on their friends list or is in the same chat room, but means you will almost never complete a game with random people.
Resync issues are more annoying, with things like permanently losing your spy agency happening last game. These sometimes can't be fixed by reloading.
As for the balance issues that TommyNT pointed out: these are a little overblown in my opinion. The free settler is very powerful because of the strength of artists, but skipping those virtues and hard-building/buying your settlers can often pay off, since having 3 extra tier-3 virtues can be a big boost in the mid-game. The game is incredibly fun when you can actually get it to work. It just isn't Civ5 BNW.
I am hopeful that the issues that do exist can be fixed through modding, now that someone has figured out how to get XML mods to work in multiplayer. I'm going to try testing out some mods with my friends, and see if that improves the game.