Putting dialog cleanly in the lower-right section does help. There is an issue though when you are speaking with NPC's the last thing said isn't always at the bottom of the log:
This bug happens occasionally, but when it does you still have the option of going to your journal (default "L" key) and following the dialogue in the "Dialogue" tab. Obviously it would be better if that were not necessary and the bug were fixed, but until that happens it's a usable workaround (and hardly a reason to "avoid co-op").
I've been playing D:OS mostly co-op and having a blast and practically no co-op related issues. Frankly, it works a lot better as a co-op game than a few titles in the past years that have billed themselves as being primarily built around co-op play.
