Let's make a list out of this, I'll start:
1) You find out about every little lie they told you during the relationship.
For example, I just found out yesterday that my first ex lied when she told me I was the first guy she ever gave head to... why would I need to know that!? She just ruined a happy and somewhat innocent memory from my past.
2) 95% of the time, one of the two isn't REALLY "over" it.
I never get along with an ex for more than a week because one of us will inevitably get MAJORLY jealous about something and make a big scene. It seems like certain dynamics usually don't go away
3) Your ex's over-confide and tell you things you don't want/need to know.
This is sorta like #1, but more general... my one ex told me the other day that she's slept with FOURTEEN guys since we broke up and is sick of being called a slut and not being able to really deny it. Sweet, I feel not at all like a chump for dating you knowing that it was that easy all along... some things are better left unsaid between ex's, and the more they talk, the more likely it is that these things slip out.
Feel free to add on!