I think that these following changes in the multiplayer mode would make the MP much more enjoyable (and a few bugfixes):
1. An option in preferences to allow all the popups as in the normal game. It's quite frustrating, as enemies can even capture your cities without you noticing it. It's also pretty tiresome trying to remember all the 15 finished buildings and their locations in the 10 seconds that the list in the upper left corner is visible. If it's supposed to make the MP-game faster, it doesn't work. It's actually making it slower, as you must browse through your cities fixing this and that. It should atleast be made optional!
The popups that I think are crucial:
- "What shall we research next?" (I rarely agree with the AI

)
- New build orders after an improvement has been finished. This is perhaps not needed when a city completes an unit.
By the way, I don't have the "fewer multiplayer popups" checked.
2. The game shifts the view elsewhere whenever I attack. The result is displayed in the upper left corner. This is quite annoying, if for example you have 50 tanks ready for assault and every time you attack with one, you must then scroll the window back to the units (or mouse-click) and choose another. The scrolling hardly makes the MP-game faster!
It would also be nice if the game would show the AI moves whenever they cross my borders (so that they won't get next to my capital without me noticing it

) or attack my cities.
3. If you use the "goto"-order to an unit, the game chooses another unit automatically even though the unit's turn is not over. It does of course get to move the rest of its remaining moves later, but this is highly annoying when, for example, building railroad-systems and such.
And the bugfixes:
4. The AI
always declares war when you don't give them what they demand (as in normal game most of the threats are simple bluffs) or if you demand that they leave your territory or declare war. I don't know if anyone else has experienced this. This is in LAN Turn-Based game.
5. Always renegotiate deals doesn't work in MP. It simply announces that "we have lost our supply of spices" and you lose one turn of happiness.
6. Sometimes when you trade across water with harbors, the deal is suddenly cut off with no reason. You are able to make the deal (say, buy dyes) and it works fine for two turns or so. Then it (without any declarations of war or trade embargos or such) suddenly simply ends. No dyes

. You may buy it again, but take the chance of it ending again. I have found no reason for this and it is only in MP (as far as I know).
It will probably be enlightening to see what many have thought of these issues here (some of them quite temperamentic

)
http://forums.civfanatics.com/showthread.php?s=&threadid=59432