Some of the connectivity issues (all during custom games):
Sometimes 2 people in the game lobby are red 0ms even though if you look under connection info, the two people are both in each other's 'connected to:" list. If they're not connected to each other they are almost always going to be red 0ms, but I've had it happen even when both were 'connected'.
I also noticed that usually when 1 person tries to reconnect to the server due to a red 0 ms person, they'll still stay red 0ms on a second or third attempt to that same person, But I've only seen a small number of rejoins (5 or 6). I can't remember if anyone got non-red by reconnecting.
#2 During matches, I've had about 7 out of 10ish matches have drop-outs (network related, not manual quitting). I've had 0 drop-outs prior to the day 2 patch (day 0 games were all fine once in-game). I know Stardock said the lag timeout tolerance will be addressed soon. But it's not usually 1 person lagging or dropping out, I've seen servers drop half the players at once, and one half of the server still remains connected. It usually happens within 5minutes after starting a game, when demigods are in the level 2-5 range. It's hard to chat with players after the fact, but I know one game 3v3, three players dropped out instantly and me and 2 others still remained in the game. Another 4v4 game today I had everyone drop out from my perspective, and I talked to another guy from that game and he said that on his computer, everyone but him and 1 other teammate dropped out. A third game, I think it was 4v4 and me and 2 others remained in the game, and a second later a message popped up saying I was desynced to one of the remaining players. Although if I was desynced with that person, I'm not sure why that person didn't drop out when the majority did.
#3 random NAT server disconnects while trying to join games or in lobby, can't really provide more info than that. Usually going back to menu and logging back in fixes it and brings back the connection info screen.
#4 There's still some random timeouts for players while waiting in the game-lobby. Usually it's red 0ms related, but not always.
#5 It doesn't seem to be happening anymore, but early day 2 when I had connection info open for a short time, it would usually crash the game in an unhandled exception. I haven't had it happen the last day or two though.
#6 Minor issue, but in custom games list, very occasionally when I select a game and click join, it'll join me to a different game instead. For instance I see player A hosting a game and player B hosting a game. I click to join player B's game, but I end up in player A's instead. It almost seems like the server list doesn't update accordingly the odd time. (I usually notice it when I'm asked for a password even though the game I selected wasn't * marked; it joined me to a different game than the selected one). After joining me to a wrong server, if I instantly click refresh server and after it seems to refresh it'll still join me to a different game than the one I selected. But if I seem to wait about 30 seconds or so afterwards and then refresh the server list finally joins to the properly selected games.
#7 Sometimes there are one-way connections according to connection info when in game-lobby. Eg. I'll be connected to player A under my name, but under player A's connection list, I won't be listed (or vice-versa).