I'm not sure if anyone else has noticed this, but sometimes when I wake up in the morning after a dream that involved me being really angry at someone, I still feel an irrational anger for 30 seconds or so. I always remember it's just a dream, but it really feels weird. :?
I've had that too. Only less with anger, more with sadness. Like about a month ago I had a dream that I watched my best friend die (probably from some sort of drugs or something, as she was acting completely insane up until she died) and when I woke up I had this feeling like "She's really gone..."
I've also had that feeling about other people even if my dream wasn't about them. (they didn't die for real. IDK why I felt they did)
I guess it just takes a little while for your mind to realize that your dream isn't neccessarily reality.
My ex-bf used to dream that I cheated on him, and then he would be shitty towards me for the whole day. I mean, wtf, lol. That really pissed me off. :P I think it's natural though, sometimes dreams are just so realistic or hit a really sensitive nerve. As long as you don't let it affect you for very long I don't really see a problem. And definitely don't let it affect how you treat others. Compartmentalize emotion.
Ah, I know the answer !! It's a little part of the brain called the Amygdala, that controls terror and aggression, and it can get activated in REM. That's what causes nightmares or really animalistic anger.
Sadness or other emotions are from the part of the brain called the Limbic System, or the Mammal Brain - the layer right under the Neocortex (the Human Brain). The brain is made like an onion in layers... there's what's called the Lizard Brain which is basically just a lump of brain tissue attached to the spinal cord, then the Limbic System build around that from the next evolutionary stage, and then the Neocortex is a thick layer of brain tissue around that. Each is more advanced and intelligent than the last.
Each part is still active... it's like evolution can't shut them down but can only build new layers over them and suppress some of the functions of the older systems. The Lizard Brain (I forget the scientific name for it) is essentially the same as what powered the dinosaurs, and is responsible for aggression (I believe the Amygdalla is located there). The Limbic System or Mammal Brain is the home of love and other emotions, and the neocortex is the center of logic and intelligence.
An oversimplification, but then I'm going completely off-topic by now anyway and really really need to get to sleep!
That is why it is important to develop dream recall, so you can realize why you are feeling angry at the person. I remember learning about this it was like a great epiphany! Because my girlfriend at the time and I didn't get along because of her moodiness. She would wake up on the wrong side of the bed or I would. Then I cultivated my dream recall and discovered what you are talking about and it really helped me. Awareness heals.