I agree regarding the grammar. After living in England for a couple of years, mainly surrounded by native English speakers, things just either sound 'right' or 'broken'.
Although opportunity of living here is somewhat luxurious for many. So I would say that listening to as much native English as possible is really good for grammar :)
Exactly, you can get that right/broken gut feeling just being immersed in that language for thousand of hours.
Regarding real immersion (both listening and speaking) maybe personal tutors via skype or language learning communities could be a cheap alternative, i've never really tried this approach (lazyness) but i've thought for years it could have been worth the price.
Although opportunity of living here is somewhat luxurious for many. So I would say that listening to as much native English as possible is really good for grammar :)