Here is a list of logical fallacies. It's not comprehensive, but it's a start. Try to avoid using these.

Non Sequitur: when a conclusion does not follow from its premises.
Begging the question (circular reasoning): when a conclusion is assumed within the premises.
False Dichotomy: when a choice is erroneously limited to two options when more are possible.
Slippery slope: when the triggering of one event is assumed to trigger more without probable cause.
Ad hoc: an unprovable claim.
Argument from ignorance: the assumption that the interlocutor's ignorance of data is proof of an alternative.
Appeal to tradition: the assumption that things should remain the same because they worked in the past.
Argument from person experience: the act of relaying memories as fact, despite their unreliable nature.
Argument from absurdity: taking a conclusion or premise to unconventional territory in debate to make it seem absurd.
Fallacy fallacy: the assumption that one logical fallacy in a syllogism disproves the entire thing.
Personal incredulity fallacy: the assumption that since the interlocutor cannot understand it, it must not be true.
No true Scotsman: changing the definition of a term to exclude given evidence against a claim.
Equivocation fallacy: using different definitions of a word throughout a syllogism to support the conclusion.

Most these terms have Latin names, but I don't know them all off the top of my head. I suspect Sheldon does. As an added bonus, a syllogism is the expanded parts of an argument, which shows the premises in their simplest forms.