There are a few issues with multiplayer right now.
First, it takes a surprisingly long time to connect, and there's no feedback that the connection is working. I cancelled it several times thinking it wasn't making progress. Some sort of feedback "Trying to connect...." would be good, and better still be some real feedback about the connection state (sending handshake; acknowledgement recieved, initializing game state, etc... You can even include silly ones like "Waking up the Devourer Golem" that way). That sort of feedback looks cool (to me, at least) and it can help people in debugging.
The "Connect to multiplayer" screen should show your own IP address.
Right now both arks spawn as the same gold colour.
Do you intend for players to eventually get different starting home planets?
There needs to be some mechanism for players to get Science from eachother's planets. At the moment you have to change the owner which is very cumbersome.
Clocks still get out of sync readily. I wound up with a 5 second disjoint in my last attempt which makes it feel really laggy.
Hopefully something better can be done with multiplayer in AIW2 than we had in AIWC. One of the largest reasons I didn't try to get more of my friends into AIWC is how miserable getting over-the-internet multiplayer to work (I don't think I have any friends who know how to do things like "open a specific port on your router", or "how to enable port forwarding"). There was some discussion of NAT punchthrough during the kickstarter; any chance of that actually happening?
