Pros
BP pays well above market, which is great while you are there. It may haunt you in future job searches. Upstream BP is very good at what they do, finding energy. IT is weak and misguided but that provides opportunity for smart people to do great work. There are some great people at BP, diamonds in the rough, who can make it a great company someday if they can effect change on the culture.
Cons
BP management pays lip service to modern corporate values but fails to change. There are so many levels of management, most of which are clueless to what other great companies are doing and yet are closed to new ideas. Powerful internal customers routinely overrule subject matter experts to get their own way. BP calls itself collaborative but the reality is a paradox where consensus is required but everyone wants their own way effectively paralyzing any meaningful change. London lives with it's head in the clouds effectively ignoring the wants and needs to employees and leaders worldwide. Ex. 9am (GMT) global con calls are 3 am US Central time...when pressed the UK leaders will respond that the meeting can be recorded and reviewed later. Happens all the time. BP wastes more money than most companies make, which has got to be hard with the price of oil so low these days.