I just got Dragon 10 last week and have been most impressed. I have an unusual accent, speak fast and sometimes mumble, but it still works perfectly as long as I speak in clear phrases. My question is, when I say "Correct That" and then "Choose 4" for example. Does dragon automatically train itself to remember how I pronounced that word? Or do i specifically have to do 'Spell that' then 'Train' ?

It learns. You're doing it correctly. You typically do not need to bother to train words unless they have unusual pronunciations.

Just adding to Matts answer... Have you tried Select-&-Say correction yet? NaturallySpeaking also learns from Select-and-Say correction but it's typically more efficient. With Select-&-Say correction you can verbally select any misrecognized word and either choose the appropriate choice or re-dictate. The disadvantage of Spell That correction is that you cannot easily dictate a correction if you don't see it on the available list.