Pros
BP has a very good training program and encourage training throughout ones career. The IT system is well done, while it can be slow, it is reliable and well supported. The biggest strength of BP is excellent people to work with; they do a good job getting good people and training them on a technical level. There is also a tendency to move people every to different groups every 2 or 3 years (this is not a relocation but a change of groups locally). I like this, but other people may not. There is also a lot of flexibility of work schedule and good work-family balance.
Cons
The main problem with BP is that it is a large,slow, and tradition bound company. There are processes in place for everything from drilling a multi-million dollar well to putting toilet paper on the dispenser. Failure to flow results in chastisement from above. If the processes says jump off a cliff, you are expected to do so. It is also nearly impossible to make change happen even if you are at a high management level. In mid 2008 there was an initiative to simplify the processes we follow. Unfortunately the simplification process is so complex it has yet to be implemented.