No huge warmonger penalties for conquering city-states
AI doesn't hold grudge against you for too long, no neverending wars
You can have Research Agreements only with close allies/Civs that you have Dec. of Friendship with (not sure which it means)
In early era sharing a religion gives a modifier to diplo, having a different religion a negative (and I bet that different leaders care for religious matters differently)
In later era religion doesn't affect diplo, but ideologies (Order, freedom, autocracy) are a modifier for forming alliances
Your spy getting caught gives obviously a negative hit, but if you discover that, for example Russia is planning to invade India, you can give a note to India and they are grateful and you get a positive diplo
After the empires main borders are established, the AI doesn't get mad for settling new cities
These come to mind
Also not directly related to diplomacy, but trades (open borders, luxuries etc) can be renewd when they end (if there hasn't been any scandals with other civ), so you don't need to click all of them again.