I'm from the UK, and if something is wrong, your biggest challenge is making appointments with the right people.

Some of my colleagues from the UK who have had to go and see someone in the US report that it's a minefield of: a) Checking which doctors take your kind of coverage b) Co-pays c) Ensuring you know what you are/aren't covered for d) Random bills that may appear after you visit someone, depending on whether their interaction with the insurance company