The newest version is 3.9 (incidentally released today, also see here
but apart from that you can also try and compile the game from the newest source code in the svn (read the compile page
for this), which is what you'll need to do to contribute to programming.
On the speed, the first thing you mentioned, the calculations at the end of the turn, for what I know this wasn't the AI calculation but the resolvement of the AI orders, because it simply submitted too many of them. You can produce the same effect by adding several dozens of items to the production queue, but this has been fixed with the first attempts of a real AI, so it shouldn't appear in new versions.
The other thing, the graphical interface, there the time isn't lost in the interface but mostly in some calculations like the remaining time in the production queue, these could be improved but I believe the general consensus is that they probably will be changed again several times anyway. So the main focus now is still on integrating new features, as long as the game is playable for tests, speed improvement, hunting bugs and memory leaks and all those things still have low priority and will probably mostly be done somewhere in 0.9. (At least this is my oppinion, if geoff or tzlaine tell you something otherwise they are the ones who are right)