Pros
The people are great and really care about their job. American, and the airline industry in general, is not a lucrative business, but most of the people are there because they care about the company and the business. The airline industry is fascinating and it gets into your blood, so it's very difficult to leave. In theory, the travel privileges are a nice bonus, but because everything is stand-by, and planes are so full, it's hard to get a seat. If you really want or need to be somewhere, it's best to just buy a ticket like everyone else does.
Cons
It's an incredibly bureaucratic place with many layers of management. Approvals are difficult to secure. Meetings often focus more on discussion than action. It's easy to see why the industry is struggling because it's physically impossible to move that many people to change when you are not a nimble organization. I mentioned the travel privileges above - this is something that is sold as a benefit but hard to realize. The other negative is the poisonous relationship between the labor unions and management. This is something that appeared to be improving until recent years when it hit the skids and it's now in the cellar. I'm not going to take sides in the argument. Bad relationships are the fault of both parties.