Somehow, I never fell when I first using clipless pedals. But, about a year later, I did fall in the middle of a busy intersection at a light (Rt. 117/62 in Stow). It's one of those little uphill stops that I now hate at all costs. I have never gone through this intersection again, unless I am turning right and don't have to stop! Eight years later...
I always unclip with my left foot. I just lean a bit and unclip a little bit ahead of where I think I will need to. It never occurred to me to try and unclip with both feet. It's funny, I know I started unclipping on the right, but I switched when I read something, can't remember what. Now, I absolutely cannot unclip on the right, which I know is bad. I am definitely left footed; in fact I can barely walk my bike from the right side. It just doesn't feel right. On the other hand, I can unclip on the right when I am mountain biking, but I think that is fear of killing myself, so I am prepared for any emergency.