I've often struggled with the use of the words 'respect' and 'dominance' around horses. I don't think horses 'respect' people - it's a human concept and calling a horse dominant or deeming that he lacks respect seems to be an excuse for being tough with them.
Mark gave a really good example of where the idea of 'respect' gets you. If you teach your horse to do a turn on the forehand, moving his hindquarters away from you, that would seem to be respectful and means that you are a good teacher! However, if you have a horse that walks into you, you could think that you have a horse with no respect for your space. However, the opposite is true. Most people inadvertently train their horses to come right up to them by over-petting the head, cuddling him or just not asking the horse to step out of the space. Stepping into your space is learned behaviour. So if it is something you have taught, albeit inadvertently, is it respect (good teacher) or disrespect (bad horse)?
Incidentally, when advocates in court address the bench with the phrase "With respect your worships...." they are usually about to launch a scathing attack on their common sense. "With respect" usually means "look hear you idiot, how stupid can you be?"