Although the speech used may not always be perfect, the exact same thing will happen for those learning English - it happens in every language.
Take the words "could have", most of the time it's pronounced more like "could of". This happens so much that people actually use the latter and think it makes sense, even though it doesn't.
I agree. That's how I hear it too. In general I was complaining to my Russian husband about how spoken Russian sounds so different than how it sounds if you slow it down and pronounce it as written (not even mentioning the Os that sound like As. There is a rule about that).
I did find a helpful site - it's called Russianpod101. They have audio lessons that you can put on your iPod. The first ones are free. They sometimes slow down the speed and you can really hear everything enunciated nicely. (Other than that I don't like them much). =D