Minhag vs. din

When a Jewish community's practices disagree with your הַשְׁגָפָה, sometimes it's possible to point a finger and say "but that's minhag, not din." An example that even my non-Jewish readers will be able to sympathise with: Reb Tevye getting so worked up about his daughters making their own matches in Fiddler on the Roof. (Indeed, something which would be lost on non-Jewish watchers of the film is that the reason he was willing to compromise with his first two daughters, but not with his third, is precisely because there the issue crossed the line from minhag to din.)

It's easy to say this, but what exactly marks the line between minhag and din? Outside of Orthodoxy the answer's clear: you have rabbinical assemblies, with law and standards subcommittees, to which responsa are submitted, which debate them, then either accept or reject them. Inside Orthodoxy, I'm not aware of a formal process for determining halacha in this way; it seems to me that people publish responsa, and either the majority of rabbis of the generation accept them, or they do not. But even then, the minhag of a community is regarded as inviolable, and treated almost on par with din. An example not from a teshuva is the materials aviva_m taught herself the practice of Judaism from when she first became practising; they made no distinction between kabbalistic minhag such as which order to cut your fingernails and core Jewish practices. And, come to think of it, the (aviva_m: look away now) Kitzur Shulchan Aruch) is no better.

So what, then, does distinguish minhag from din in Orthodoxy and pre-Orthodox normative Judaism?