Fundamentally, I agree with Salmonius's comment. Most people ask another reliable authority such as a rav you know, what the kashrut reliability of a place is. In some cases, he may know and give you an answer. You can ask the rav, directly, why he has arrived at his conclusion, but, unless his response is obviously "un"halachic or has no related basis (e.g. he says, "No, you can't use this kashrut because the supervising mashgiach disagreed with a Rash"i we discussed during chevruta) you would be bound by the rav's decision.
If that option is unavailable, most people I know hedge cautiously. In other words, they just don't use products under that supervision until they can find out reliably that they can.
The point is, that kashrut rules are extremely complex for the lay person. This applies even to more notable organizations such as the OU. Case in point - you'll find a few M.Y. questions regarding OU - dairy designation on products that don't seem to have any dairy ingredients. Previously, there was an OU DE (Dairy equipment) on such products. A few years ago, OU eliminated that designation. Does this mean that as a lay-person, I can assume that by reading the ingredients I can decide it's really not dairy without asking the OU, directly? Answer is, no. Because, in fact, a product can still be dairy even if there are no dairy ingredients listed. That's why you and I need to hedge cautiously on kashrut items that we don't know much about.