I think I have this figured. For one let me start of by saying that my XP install is always up to date.
Now, I would get the occasional minidump back in 1.03 but they were very rare. Then I updated to 1.04 and quickly started a game with my buds. No problems. However, the patch had turned off some of my graphic affects settings, specifically the "BLOOM" affect. So before the next game I turned it on. We tried five or six times to get a game going but every time after about 10 minutes BAM, minidump crash. Like clockwork. Was getting really frustrated and was thinking about reinstalling. However, being that I am a software engineer by trade, I was trying to figure out what was causing it. Was it time or event based? Some more trials ensued and I started to realize that it crashed almost immediately after my fleet reached the first planet i wanted to colonize. Not an asteriod but a planet. That and the fact that my very first game worked got me thinking about what had changed. I turned off the "BLOOM ENABLED" setting and TADA! Not a single problem since.
Something about that setting was definately causing my crashes. If you are having similar issues to what I described then I suggest making sure that setting is off.
hope that helps.