The Senate has a lot of hardcoding put into it with missions, popularity, etc. It all disappears when you play as them so there will be some problems. As mentioned by Lofman, it will crash when you go to the Senate tab.

As time goes by you're more likely to CTD. I also remember reading about something tricky with ending the campaign, but cannot recall exactly what. Perhaps a smarter member could help me out on this one?