Summary: the problem with Pascal's Mugging arguments is that, intuitively, some probabilities are just too small to care about. There might be a principled reason for ignoring some probabilities, namely that they violate an implicit assumption behind expected utility theory. This suggests a possible approach for formally defining a "probability small enough to ignore", though there's still a bit of arbitrariness in it.
In the I-am-undetectably-insane scenario, your predictions about the worlds where you're insane don't even matter, because your subjective experience doesn't actually take place in those worlds anyways.