I don't have a link handy right this moment, but I understand that there is research indicating that the kind of multitasking you're describing is associated with a negative effect on mood, whereas acting mindfully is associated with an improved mood. Everyone is different, but I have also found this to be the case in my own life.

On a more practical note, I just find that I make more mistakes when I'm not paying attention to what I'm doing. And as for planning for the future, how much extra time would it really take if you saved it for after the dishes? A couple minutes?

All that said, I still listen to podcasts while doing chores...