Pros
BCG gives you the opportunity to have a great deal of responsibility at a very early early stage in your career. As an entry-level employee (Associate or Consultant depending on previous experience), you are critical to the success of or projects that have very high visibility with senior executives at major corporations. While you might not interface with senior clients as often as the partners with whom you work, you develop deep contacts within organizations as you formulate and implement recommendations. Furthermore, the culture at BCG is very non-hierarchical. Debate with more senior members of your case teams (including partners) is encouraged, and the hypothesis method discourages blindly applying existing frameworks to new problems.
Cons
In my experience, the most negatives aspects of working at BCG are related to lifestyle. While the firm's leadership has admirably tried to instill a culture that encourages time away from work, in practice the lifestyle can be very difficult. Team members typically work into the night during weekdays and often can have a significant amount of work pushed to weekends. Moreover, many consultants spend four days per week on the road, often traveling significant distances. Unfortunately, the travel requirements typically do not diminish as you grow more senior, as partners often have clients in several different cities that they need to visit on a regular basis.