I did a lot of work with IBM Via Voice when it first came out and was better supported than it is now. From what I know Dragon Naturally Speaking is the product of choice now but although I was given a copy I havent been too inspired to roadtest it.
Yes you do need to train the software and based on my Via Voice experience accents are a real issue as the bias is towards American English. In the end I found that the time I spent (and I worked hard at it in work settings) wasnt worth the effort as I could simply transcribe the spoken text on a word processsor quicker than the voice software could do it.
Another source of error was in using the headset mike. You can calibrate the software and hardware fairly well but the next time you run a session, you cant get the headset in exactly the same position it was the time before. That meant more time wasted calibrating.
Oh and on top of that the worst things was that there real problems with phonetic howlers. That meant spending more time doing some really close proofreading for contextual errors that spell checkers couldnt pick up.
I'd love to find a program that did the conversion well but I dont think its there yet.