Pros
You'll be working with a lot of very smart people who care about the work they do. Because it's such a large company filled with these intelligent people, you'll gain a lot of experience and skills that you can carry with you throughout your career. On the other hand, it is definitely a stable job- I say that because I've noticed it is pretty difficult to get fired just for under-performance. They really try to retain their people. This is very specific to what team you're on, but there are many teams that are good about work/life balance and managers who don't want you working too late if possible or on weekends at all. Specific to the headquarters, the office location is awesome for commute and nearby dining. If you're looking for a job to impress the stereotypical baby-boomer parents, working at one of the business offices is for you.
Cons
Most pros and cons are heavily based on what team you are on, so I will try to stay general. It is a pretty bureaucratic system, despite the company trying to make it seem like the culture is "different" and "special". The pay is not as good as other healthcare companies, but they try to make it seem like the benefits make up for that, which is not really true. Promotion paths are slow unless you play the "game" of bureaucracy well or have a management structure that cares more about work product than your tenure.