The "MGH mystique" is of course not real, though many people including some MGH residents and attendings swear by it. For practical purposes, if you come out of your residency able to practice anesthesiology and become board certified, you got a good education. In that respect, MGH is nothing special. Don't get me wrong, there is a HUGE difference between an MGH residency and a residency at some community hospital where they regularly have trouble renewing their accreditation because they don't have enough cases to go around or enough faculty publications to be academic enough (and I interviewed at some of those too). But I doubt there is a huge difference between MGH and, say, Brigham or Columbia or Hopkins or Stanford. If you're deciding among big programs such as these, just pick the one you want.
If you're focused on Boston programs and trying to figure out how to order MGH, BWH and BID on your rank list, honestly I think all are decent places to work (lifestyle-wise) and people are happy at all three. If you rank BID first and match MGH instead, I still think you would be surprised how happy you are at MGH, and a lot of values (i.e. "friendly," "Harvard with a heart" etc) which people rank BID highly for are also to be found at MGH. Many people at other programs have a lot to comment about the MGH "malignant" myth, but most have never actually spent time at MGH, or only passed through for a day of interviews.
Time off is three weeks vacation and one week meeting (applicable to board exams such as Step 3 as well as conferences), totaling up to 4 weeks off per year. Book budget is $500 EACH year, totaling $1500 for the course of your entire residency (applicable to PDA but not laptop or board examination fees). As far as I am aware, CA-1 call is moderately less frequent than senior resident call at many residency programs, since as a CA-1 you are eligible only for main OR call and as you get more senior, the main OR senior resident pool shrinks because other senior residents are off doing cardiac, OB, etc months. CA-1s at MGH seem to do main OR call 3-4 times a month; I'm guesstimating that CA-2s and CA-3s may have main OR call maybe 5-7 times a month. Either way, it will be a breeze compared to your Q3 or Q4 surgery or medicine colleagues.
About passing the boards, and possible weaknesses in case numbers etc. You will find that wherever you work, some things are stronger than others and MGH is no different. We have stronger rotations and we have weaker rotations. That's the nature of any hospital. Don't be fooled by anyone who tells you "Our residency has no weaknesses." Regional experience, for example, is considered a strength at only a few hospitals across the country; in all others, it is not a strength. So it's a no-brainer, regional is not an MGH strength. The cardiac rotation is also not a strength and hasn't been for years and years. If you go to another residency program (Stanford, Duke, etc), maybe the weakness won't be cardiac but if it's not, it's probably something else. See if you can elicit what it is by asking around. Sometimes the residents will tell you. Sometimes they won't. When you are looking around at programs like MGH, all will have strengths and all will have weaknesses (and some don't tell you about their weaknesses), but your education is generally more than adequate.
About passing the boards, last year was the first time in a long time that people have had trouble. Prior to that, Dr. Baker used to stress that "Everyone passes the boards." I don't think there has been any major change in teaching at MGH so I can't offer any explanation for why. Dr. Baker said the same people also had previous red flags for performing poorly on their in-training exams in years prior. I do not personally have any major personal concerns (besides the usual medical student / resident exam angst) about passing my boards.
About the personality of the program director, this is something that I think needs to be put in context. We have a very large anesthesia department, I have no idea how big but to make numbers even let's say there are 100 attendings. When you hire 100 people, you get a huge variety of personalities. At one extreme of the bell curve, there are a few old-school alpha personalities and I suppose the PD is one of those. At the other extreme, there are a few attendings who show up to work, surf the internet over coffee all day, and then go home. In the middle are a greater majority of ordinary people who are mostly sincere, conscientious, and generally nice (as much as at any other place, anyway), many of whom also have families and other priorities outside of work. Dr. Baker is a good teacher and offers very sound, practical advice for your residency. He may not be Mr. Family Guy, but I think he is a strong PD, has a clear vision and has obviously thought a great deal about what works, what doesn't and how to improve the residency program. If you want advice on which local public/private school to send your kids to or recommendations for a contractor to fix your house, residents don't naturally go to Dr. Baker but there are 99 other attendings who can elaborate on these topics (and believe me, they do, sometimes at great length).
Are we an intense and hard-core program? Yeah, probably. I think we work very average, reasonable hours (generally relieved from your OR case at 5pm if it's still going) but the MGH program is 'intense' in that both faculty and residents are very enthusiastic about anesthesiology and take it very seriously. You don't have to be a workaholic to fit in. You do have to love anesthesiology. We all want to go home at the end of the day, but while you are at work you should relish every opportunity to discuss academic topics or take on challenging cases. That's what I think is the good thing about MGH, you get to soak in a lot of environmental enthusiasm about anesthesia while still having a pretty decent lifestyle and average work hours.