So, I have had this problem for some time now.
As soon as I get a certain amount of influence, or a certain number of planets flip over to me, the minimap stops repainting correctly and it eventually turns completely blue.
One game it did not act like that. There was only one thing different that I did that time.
I limited the game to a single CPU.
So in this last game when it started to do it, I saved the game, exited, restarted GalCiv, went into task manager and set affinity to CPU 1. Then I loaded my game and continued.
The problem never resurfaced, and after about 2 hours I won with an influence victory.
So, if the devs take notice, are you guys running dual core Intels?
You say you have not really seen the problem, and it also seems to be related to my dual core processor.