Pros
I've been at BP over ten years now. As a long term employee, I have my share of petty gripes about the company. But overall I can't complain. I believe the company genuinely cares about it's employees, the pay and benefits are excellent, and the work-life balance is good. And the people I work with are great.
Cons
In some areas of the business there are still good 'ol boys networks, but it seems like the company is working hard to dismantle them. Unfortunately there are still some mid-level and higher people who are only in their roles because of their network. Sometimes personnel policies can be pushed aside for convenience. For example, even though most roles are supposed to be posted and competitive - and employees are expected to be in a role for at least two years - some employees (one's who are deemed to to be "special" by management) are given the role through "facilitated moves" and the two year rule is ignored. For the rest of us mere mortals, we just have to suck it up. It's not a widespread issue, but it can cause some discontent when someone is given a plum assignment over many other equally qualified people who weren't even given a chance to apply and interview. One other con is that the company is continuously reorganizing. In the last ten years I've lost track of the number of reorgs. Every time new senior management comes in it seems that the old organization is ineffective and needs to be replaced. It's happening again as I write this.