Informal fallacies get thrown about a lot, but it’s not always clear how they are corruptions of reasoning. But conspiracy theories do seem to be a real corruptions of reasoning.
Conspiracy theory requires something more than a secret plan to do something unlawful or deceptive. Any group of drug dealers or petty criminals does this, and there are certainly more glamorous spy-movie style historical conspiracies, like the burning of the Reichstag. But the recognition that there are such things does not usually get called a conspiracy, and believing in such things is not the sort of thing that makes for conspiracy theory. Conspiracy theory only seems to kick in when there is a substantial body of patent evidence against the conspiracy: The Warren Commission report, the consensus among specialists for Stratfordianism or climate change, the NTSB incident report of TWA flight 800, the 9-11 commission report, a pile of evidence for Obama’s native birth, extensive studies showing no link between vaccines and autism, O.J.’s blood at the crime scene with a single glove seen by 14 cops and an eyewitness who saw him fleeing the area, etc.*
The fallacy of conspiracy thinking can be seen from the fact that it is a way of reasoning that has never borne fruit. None of its gun show, “shocking truth of the real story” narratives has ever set out a case that came to be seen as true. I stress that it is a false belief in logic, i.e. about the way to the truth and about the nature of truth itself. It is a sad thing to watch those who suffer from it.
*I leave aside the various economic conspiracy theories since they all seem to be based on a much simpler mistake of assuming that the economy is the sort of thing that can be controlled in any sort of precise, function-machine like way.