Conspiracy theorists like to talk about the use of critical thinking, but there are some fundamental red flags that come with any conspiracy theory which should automatically put rationalists into cynicism mode.
Critical thinking is the ability to take a conventional fact or idea designed to be accepted at face value, and consider the history, motive, messaging, source, relevance, completeness, factual support or lack thereof, and purpose of that fact/idea. It's an important skill for scientists in particular (and writers) because it means that you're always verifying information through evidence.
When a conspiracy theorist talks about critical thinking (as karajorma said) they discard evidence which does not support their assertion, and focus on pieces of evidence that might.
Conspiracy theory is not unlike the standard method of legal defense - it's not about one damning fact (because that can be easily verified). Instead, is focuses on building doubt in a person's mind by presenting small pieces of fact without proper context or fitting them into the larger picture. Very good conspiracy theorists use misdirection as well, and will often circumvent hard facts they cannot question by presenting pieces of information in the periphery that allude to problems with the larger fact but, when taken in context, are usually meaningless.
The 'best' conspiracy theories take a fact with massive amounts of evidence behind it and tweak it only slightly to suit a political purpose. Thus they turn what should be a straightforward issue into a matter of perspective, and work to skew the perspective of the individual reviewing the conspiracy theory (which is a fairly simple matter).
Conspiracy theories also have a target audience. They're not suited to convincing will-informed rationalists or people who will conduct independent verification. Instead, they target people who often have a fundamental distrust or mistrust of social conventions, norms, people, or governments and a predisposition to belief in unverified truths (schizotypal personality traits - we all have them to a degree).
Quick and dirty ways to identify conspiracy theory:
1. Claims that there is a hidden truth.
2. Evidence is presented in a biased way (focus on one side of the argument).
3. Evidence focuses on a wide variety of small-picture ideas and criticisms and does not include strong core arguments.
4. Theory starts with the premise that the broadly-accepted story is false.
5. Theory deconstructs a mainstream theory, rather than building its own interpretation based on evidence.
6. Theory overlooks or circumvents core facts of a mainstream argument through circling.
7. Tautological reasoning (circular logic - elements of the theory rely on the truth of other elements they've presented).
8. Claims that the theorist has identified something no one else has identified.
9. Political motives that contradict a social or political movement.
10. Charismatic central figures that repeatedly attempt to convince the viewer of the truth of their claim rather than relying on strength of evidence.
I like conspiracy theory in fiction, I just don't like it in society because it preys on people who are unable or unwilling to research information for themselves but who are predisposed to believing in causes. They're closely related to cult phenomena - the same sorts of people fall prey to both.
