The best aspects:
1.) You are treated like a first year employee and are given meaningful work
2.) It's a refreshing combination of quantitative and qualitative work
3.) The work concerns high stakes litigation, so everything actually matters
4.) Management is very transparent
5.) Management cares about developing lower level employees and takes into account what sorts of projects they want to work on
6.) The intern class of 20 is big enough to have a community but small enough to get to know everyone well
7.) In general the people are very, very supportive and friendly
8.) BW works in a variety of practice areas, which provides more opportunity for novel work
9.) You work closely with PhD's in economics and math - which provides invaluable learning opportunities
10.) It's an interesting blend of law, math, economics, and even a bit of computer science (for cases involving models that have to be fast).
11.) There were a variety of fun events that HR planned for the interns such as dinner and sailing trips.
12. The pay is competitive
13.) DC is a fun city for twenty-somethings
...the list goes on
My only complaint is very specific to me. I am very interested in computer science and wish there were more cases involving c++, python, etc. Otherwise, I sincerely had 0 qualms.
Advice to Potential Interns
In my opinion the two defining characteristics of Bates White are that it is an economic consulting firm and the manner in which its relatively small size and culture make it different from other economic consulting firms.
Characteristic 1: Economic Consulting
Econ consulting is much like traditional consulting - there's a lot of novelty from one case to the next, soft skills like client management are important, etc. However, econ consulting requires less travel, involves a more quantitative skill set, and is much more academic. For example, upper level management consists of PhD's in economics and math as opposed to MBAs. It's about as technical as you can get while still being in business consulting. So if you are interested in business consulting but things like math, programming, etc. Economic consulting might be something you'd enjoy.
Also, as far as I can tell, Econ Consulting is a booming industry and the competition isn't too intense because of high barrier to entry (it requires a large group of people and experts with very specific experiences). So now is a good time to be in the industry (as far as I can tell).
Characteristic two: Bates White Culture
Bates White was founded by consultants who felt constricted at other firms and academics who felt constricted in a university environment. I think that is reflected in how much control they allow lower level employees over their own careers; if you want to switch to a completely different practice area they will work with you to do so. If you want to learn a specific skill, they will help you find an opportunity to do so. This can be very appealing.
The founders who had previously worked in consulting did not enjoy the "eat what you kill model" characteristic of other firms; they wanted to work in a collaborative environment and not one in which everyone was trying to protect their own business. Consequently, they have gone to great lengths to make BW a community that is tight nit, friendly, and not isolated by practice area. So if you want a tight nit community, BW might be a great choice. The downside is that they are relatively small with really only one office - so you lose a few things. For example, if you want to relocate to a different city, you'll have to find a different job because there's only a BW office in DC. Whereas at a bigger econ consulting firm like AG you could transfer to a different office.
Another downside of the small size is that not as many people have heard of it, although everyone in the industry knows of BW. So if you are looking for prestige, BW (and actually econ consulting in general) is probably not for you.
Advice to Management
At the moment they are crushing it, and I sincerely have almost no suggestions. Of course more vacation days, higher pay etc. would be desirable, however I think they are fair. For example, they pay entry levels about the same as top strategy firms, but expect you to work less for the same pay (on average 45 to 50 hours per week vs 55 to 60). Also, you can get paid additional money for working more hours, so if you do end up working as much as you would at a top strat firm, you will get paid much more (You can clear 100k as a first year employee if you work 55/wk).
My one qualm is that they give you very little time to make a decision on their offer following the internship - you are given two weeks, whereas many companies give you several month. I think this can generate some resentment, because it limits your ability to evaluate all your options.
Sample Interview Questions
When I interviewed I had two cases and three behavioral interviews.
Example case: One of the cases was a fictional case about a boxing association that was being sued by retired boxers who had health complications due to their boxing careers. The questions concerned estimating how many cases were going to materialize in the future, how much money to allocate to those cases, and working out the expected value of settling vs. going to trial in different cases. It required a lot of quick mental math and some knowledge of stats and probability.
Behavioral: Why econ consulting is a huge question that was emphasized and repeated several times; they want to know that econ consulting isn't a backup for investment banking or strategy consulting.