When playing in co-op multiplayer; The need for a Conversation log is dire.
It is very hard to read the text the NPC's speak, and I can't read (hear?) my friend say his words, and if he is a fast reader, I won't have anytime at all to read what the NPC is saying.

If my friend runs into conversation on his own, I don't want the conversation log to notice, I'd rather have it role-played between characters OR partly recovered when meeting one's friend. As the information would be on hear-say only and not firsthand.

That being said, any type of conversation log would be a great improvement.