So far, I've noticed that turn times maybe start out a little bit slower, but they don't seem to grow in length as the game goes on like it used to. The only bug I've hit so far is that sometimes while processing Next Turn, Civ V will zoom to some particular part on the map for no reason. Once AI processing is done, zoom. Goes right back. Annoying, but not a big deal.
I'd try other DirectXs, as that might be the issue. Also, of course, upgrade your drivers.