Question about accents of actors

I've been puzzled by one thing for a longer time and perhaps I'll get an answer here.
You know how Renee Zellweger was casted as Bridget Jones (a gal from Texas as a Londoner) or Russell Crowe as John Nash (an Aussie as an American).
So, I'm wondering if native speakers of English notice/are bothered by their accent not perhaps being exactly the one it should in the roles?

At least I (a native Finn) mostly notice and also sometimes am bothered by the way how -say- an actor from the South tries to pass in a film as a reindeer farmer from the North. They seldom manage to catch exactly the correct accent of the local version of Finnish.

Ok, it may be silly to get annoyed of the small difference in the accent, but it just makes me wonder how these big stars are managing according to the ears of an English speaker.

[Tdol]

It depends a lot on the quality of the actor. Many actors can do the job well. In British films, American stars help the box office potential as they make the film more viable for the American market. When the accent is bad, it can ruin a film.