Pros
Opportunities to expand your career are definitely out there. BP is too large for me to speak for all locations, but where I work is full of skilled, congenial, cultured people. There is a sense of pride which helps drive people to perform well, and also a healthy measure of focus on safety, including a goal of not harming the environment.
Cons
The corporation is positively massive. There is a mountain of red tape and levels of management, and sometimes ineffective or outdated policies. In recent times there have been a multitude of reorganizations, which can make the complexity (and thus frustration) absolutely overwhelming sometimes. People respond differently to challenges, but I have had many a day fighting against lack of motivation due to the inefficiency in some areas, particularly Information Technology management.