Lots of other folks have weighed in on the subject, and while I felt some obligation to the non-Newenglanders who drop by, I didn't think I had much new to say. I doubt that what follows is entirely original, but it may offer some new lines of thought for you.
First, a bit of regional history and description. While Massachusetts is indeed a notoriously liberal state dating back several decades, it is not uniformly blue. There are a few areas that are so intensely liberal that they overwhelm the others. Cambridge, Brookline, Provincetown, and the islands may come to mind here. Boston, Worcester, and Springfield are very Democratic, mixed union/progressive/ethnic.
Vermont, once a very conservative state (remember Bing Crosby's line in "White Christmas" that it was impossible to find a Democrat in VT?), had New Yorkers and others move up there from the 70's on in search of The Simple Life. As there weren't that many native Vermonters to begin with, the state was overwhelmed and became liberal. This is important to remember because western Massachusetts - Berkshires, Little Ivies, Seven Sisters - is essentially South Vermont. (Vermont has crept over into NH as well, and the banks of the Connecticut River are now the "west coast" of NH). Central Massachusetts, and to a lesser extent the North and South Shore, have much more in common with old NH and old VT. Fiscally very conservative, socially mildly conservative, tempered by a libertarian non-interference mentality.
Those areas went overwhelmingly for Brown, offsetting the continued 88-11 Democratic dominance of Cambridge and P-Town.
Brown would be considered a RINO in many regions of the country. He is modified pro-choice (or modified pro-life, I suppose, believing that first trimester abortions should be allowed). He likes the idea of universal healthcare, but finds the current Democratic proposals abominable. He is generally frugal, but not dramatically so. He is not a crusader for anything but less spending and business encouragement. He is 30 years in the National Guard and certainly on the conservative side of gun issues and the GWOT, but not a firebreather.
Not a crusader. This is an important point in New England. He is not going to Washington to change the abortion laws (in either direction), nor the gun laws, nor the gay marriage laws. He seems, on balance, to be likely to vote conservatively on those issues, but they are well down the list for him, not highest priorities. From this we might conclude that even in Massachusetts, among generally liberal people, socially conservative positions can be tolerated, so long as the candidate is not a crusader. I think that is also true in the reverse, that conservatives will overlook or put up with a good deal of social liberalism in a candidate so long as there is not that hard-edged insistence on making the country act a certain way. Our libertarianism is a cultural preference for non-interference rather than a crusading spirit of repealing various drug, gun, or sex laws.
Brown did not run as a Republican as much as an anti-Democrat Independent. A lot of his votes were anti-Obama, anti-Coakley, anti-Democrat, anti-spending, but these did not coalesce until the Republicans gave people someone to vote for. They are latent, not automatic. In New England, the campaign stance of "I'm the normal person, those other guys are nuts" is much more appealing than any "Take Back America" approach. It is more Tea Party than libertarian or social conservative, though care was taken not to chase either of those others away. Caveat: I don't think a third party run on the same platform would have been at all successful. The stability and respectability of a major party is important.
There was a strong anti-corruption, anti-entitlement flavor from the Democratic defectors. Republicans should take note that this does not mean "We will be a lot less corrupt than those other guys" is a winning campaign slogan. This is the major area where the MSM still has considerable power - the ability to focus attention on whatever scandal they choose. Republicans have to stop thinking they can afford any.