It's the last thing anyone wants to do, pregnant or not, but you have to watch your hospital bills and EOB's to make sure your insurance is paying what it should. (Assuming you are fortunate enough to have insurance.)
I know a lot of people just accept their bills without checking because it's so confusing, but don't! Try to get a good understanding of what your insurance covers and dive in.
I went through everything with a fine-toothed comb. If I had just accepted what I was charged I would have owed over $50,000 more than I was supposed to. Not kidding! In reality I owed less than $3000 total. Between medical providers coding things wrong or "forgetting" to submit claims and the insurance company's errors, things really added up.
A funny example: the hospital charged me for Will's circumcision...and he's not circumcized!