Here are the answers to a bunch of your questions. They should also straighten out some inaccuracies:
Grades: Grades Do matter, just not as much for law students. Straight out of undergrad, you will pretty much get auto-dinged if you don't meet a certain grade minimum. Of course you're not gonna find stats to validate this, but I'm sure you can find info on their career websites talking about top-notch academic achievement. Don't believe that grades matter? Well...it's true. Try & recruit with terrible grades.
McK, BCG and Bain only actively recruit out of the top law schools - graduates from lower tiers need to seek them through career websites. But if your school also has a great B-school, then it's likely that they also advertise to the law school (if it's good).
JD/MBA:
- Consulting firms value a JD/MBA more than a JD.
- There are plenty of jobs that could use both degrees (e.g. venture capital, startups, policy).
- GMAT is not required since you've taken the LSAT (for nearly all top bus. schools)
Banking vs. Consulting: Top consulting (McK, BCG, Bain) is equally difficult to get compared to top investment banking (Goldman, Blackstone, Morgan Stanley). Prestige-wise, it depends on who you talk to. Most people in consulting outright did not want to do banking, but the same cannot be said for bankers. This is because the consulting firms that people really really want to get are McK, BCG, and Bain; in banking, you are pretty set if you get any of the top 10/15. Top consulting is easier to get than private equity/venture capital.
Human Capital vs. Strategy/Mngment Consulting: The consulting work discussed on this forum is
minimally about hiring/firing. Human Capital Consulting is a specific division within general consulting that handles this. Strategy & Management Consulting (which is what you all are talking about/interested in) deals with overall operations strategy - this is why consulting firms want JD, MPP, MS Econ, etc. in addition to MBA.
HLS & McK From HLS, there are < 10/year getting McK.
Screening/Interviews
Differences among Top 3: Bain interviews a ton of people, and offers more spots than BCG or McK (but still very few). BCG interview if you have highly competitive scores. McK interview - much harder to get; for law students, they often screen you first with a pen & paper test.
Emphasis on Case: All three put a huge emphasis on case interview. But for these firms, everyone who interviews you needs to "like" you. This is extremely subjective, and if a single one of your interviewers "dislike" you, then it's over. To that end, a surprising amount of emphasis is placed on personality - I've had friends who didn't even need to do a case in final rounds b/c they had performed adequately early on.
Traveling & Frequent Flier Miles:
Heard of cases with $100k in frequent flier miles...and $100k in frequent flier miles is pretty Awesome

High quality food, transportation, hotel covered
You travel a lot if you stick with the job. M-Th, and F back at the office. Most people exit out of the firm in 3 years to pursue management/strategy positions in industry. Depending on the industry, it's not uncommon to exit at a $250k+ salary
Compensation:
As a law school graduate, you earn $120 - $140k. You don't start as an analyst ($80k tops)