The biggest BRG-specific con I can think of is that the company pays below the market rate. This might be due to the fact that the company is only a few years old. As the company continues to grow, I hope compensation does too, or there will be a serious problem with retaining top talent. At least if you put in the time, you can receive a large bonus.
To be fair, the rest of the cons listed here apply to the entire industry as well, and they're just things you should know before entering this industry.
Lawyers. There is a dysfunctional love triangle between your team, the client, and the lawyer(s) representing the client. Lawyers love to wait until the last minute to tell you they want major changes made to the workproduct, they know no boundaries when it comes to communication (emails are sent throughout the night, and a lawyer once started calling our cell phones after hours), and they tend to make a big deal out of (what can seem like) the tiniest details. Despite this being a fast-paced environment where things get done, the lawyers can make economic consulting feel like a very, very slow and inefficient environment. You will need to be very detail-oriented and your work must be absolutely error-free, which can add a lot of stress. On the plus side, this is a good way of developing your client-relationship skills - know how to manage expectations, and make your work efficient to the point that last-minute updates don't set you back, and you'll be fine.
Despite the firm promising the opportunity to work across many different practice areas, the reality is that the variety of your projects often depends on the director who is serving as the expert for said project. Experts focus on only a handful of practice areas, so don't expect to be able to jump between the many practice areas so easily. During interviews, be sure to ask your interviewers what kinds of cases they've worked on recently, and look at the expert's C.V. to get a feel for what type of work you can expect. Without a doubt, you will also run into some very bad managers, many with the same cons as the lawyers, but with the added negative of micro-managing you. There will be many short and stressful deadlines which can result in burning out.
No matter how complex your analysis is, no matter how many hours you've spent in search of the perfect academic literature to support your argument, no matter how many hours you've put into double-checking every iteration of your team's report to make sure its 100% error-free, at the end of the day, the lawyers have the final say. Your analysis is nothing more than a bargaining point used for litigation. If you wanted to save the world or make a large impact, I don't recommend this industry.
(These are cons that occur because 75% of your cases involve litigation. If you're lucky, you may come across the traditional business consulting projects)