Today I reinstalled the game again, no mods or any tampering whatsoever. I reinstalled and promptly launched it, but the bug persists. Basically the issue is that the planets and ships don't line up with the lines that show where they are. When I am all the way zoomed in on said planet, it looks normal, but as I start to zoom out weird things happen.
I am running version 1.0.5.1028 on mac, and this is a screenshot of the issue: http://imgur.com/uHd2hYt. I played 0.90 for quite awhile after the 1.0 update and experienced no issues.