There are five broad categories into which humorous fallacies fall. The most important division is high-brow fallacies and low-brow fallacies, although there are important distinctions between the various types of low-brow fallacies.
High-brow fallacies have some error in the structure of the logic. Although they often resemble half-truth's, the elevator only takes us from the first to the second floor by way of an ACME elevator kit and some chewing gum. In brief, the humorous fallacy occurs because the chain of reasoning itself is defective.
Low-brow fallacies, on the other hand, often use valid reasoning on terms that, suffice it to say, insult more people than they entertain. They can be linguistic, allowing ambiguities of language to admit error (i.e., texting typos); or they can be humorous fallacies of relevance that omit something needed to sustain the argument (like a door open but nobody's home), permit irrelevant factors (do you like cake?) to weigh on the conclusion, or allow unwarranted presumptions to alter the conclusion reached (this concept is an example of that 4% brilliance).