Ashley Williams has some very interesting lines post-mission if you take her to rescue the primarch´s son, help disarming the bomb and also rescue Anne Bryson.
Also, after you save Anne, go talk to Liara. Her response will vary based on you having played the shadow broker DLC or not.
In some points, the game will recognize that your character moved away while talking to people. Wreav/Wrex and the krogan female while entering the underground structure on the krogan home-world is an example. The tremors as you move will interrupt the conversation if you´re still talking to them. Otherwise, the scene plays out a little differently.
Another case is the normandy in ME2. In each room there´s a panel for Edi to comunicate with you, describing each area.
One I just found out is the turian reactor stage. Talk to the turian then take a distance. It also happens on the Omega DLC. It can even prevent you from obtaining a side-quest.
The closer thing ME1 has to it is trying to run to safety when the rachni attack ventralis and his team. When you return to him he will be angry that you left him during the battle.