on reflection, i think i use three basic strategies, roughly in order of use/preference:

1) break the assertion down into sub-assertions and see if i can say anything about them. frequently, i can. this is something of a one-way test: finding something wrong lowers my confidence in the assertion much more than finding something right raises it.

2) read other people's comments -- especially those that appear knowledgeable -- on the assertion. often, even if the fine structure of the the claim being asserted are beyond me (unfamiliar terms, reasoning, or paradigm), this clarifies the coarse structure of the claim. eg: "so what A is really saying is that the old belief is wrong because B and C made assumptions we know now to be false."

3) attempt to improve my ability to judge the assertion directly. i try to avoid this because it's usually time-consuming and because i'm skeptical of my ability to apply to new skills to an important problem w/o outside verification of my skills working correctly.