Watch for the use of fallacies. Here are some important informal fallacies (following Hurley, 1985):

Fallacies in Ordinary Language
Weak Analogy: using an analogy not strong enough to support the conclusion ("Jane drives a blue car and is often late for work. Bob drives a blue car so he is probably also often late for work.").

Slippery Slope: using a claim that an event will cause a chain reaction to support a conclusion ("If you vote for the union, they will force you to go on strike, you will then lose your job, your house, and your family. Therefore, don't vote for the union.").

Suppressed Evidence: ignoring evidence that would lead to a different conclusion ("The unemployment rate is only 2% so I will be hard to replace if I quit." But the employee is ignoring that a local employer just laid off 500 workers with similar skills.).

Straw Man: misinterpreting an argument to challenge it more easily ("The union wants the contract to specify that workers can only be terminated for just cause. This means that we'll never be able to fire anyone. If someone attacks a supervisor or destroys expensive machinery, we still could not fire the employee. This is unacceptable and therefore we will not agree to a just cause provision.").

Red Herring: misdirecting the listener with irrelevant points ("The AFL-CIO wants to revise the National Labor Relations Act (NLRA). If we start revising every law it will be chaos. Business will not be able to operate if we don't know what laws are valid and what are not. Throughout history, business leaders have risked their own investments to provide goods and services to the country and have made this country strong.")

Fallacies of Presumption
Begging the Question (Petitio Principii): using the conclusion to support a weak argument. One form is circular reasoning ("I am the most valuable member of the team. I know I am the most valuable because I have the highest salary. Clearly, I have the highest salary because I am the most valuable.") and another form is ignoring a questionable part of the argument ("Unions raise wages. Therefore, unions are good." Note that this begs the question "why is raising wages good?").

Complex Question: using two questions disguised as one and then applying a single answer to both questions ("Have you stopped stealing from your employer?" Note that if you answer yes, you are admitting that you did steal from your employer at one time, if you answer no, you are indicating that you are still stealing from your employer.).

Fallacies of Ambiguity
Equivocation: using a word in two different senses in an argument, including the ambiguous use of relative terms.

Amphiboly: the misinterpretation of an ambiguous phrase leading to a direct conclusion ("The supervisor told the employee she made a mistake. Therefore, the employee admitted it." But does "she" refer to the supervisor or the employee?).

Fallacies of Grammatical Analogy
Composition: using something about the parts to incorrectly conclude that something is true about the whole ("Each doctor earns more than a nurse. Therefore, the hospital's doctors together earn more than the group of nurses." But not if there are a lot more nurses.).

Division: using something about the whole to incorrectly conclude that something is true about the parts ("This plant is very productive therefore each worker is very productive.").

False Dichotomy: presenting an either-or statement that actually has an unstated third possibility ("Either you give me a 10% salary increase or triple my retirement benefits. Surely you don't want to triple my retirement benefits, so give me a 10% salary increase.").

Fallacies of Relevance
Appeal to Force (Argumentum ad Baculum): using an explicit or implicit threat of harm if the listener does not accept the argument ("I'm a valuable contributor to this organization and I deserve a salary increase – and I'd hate to have to reveal your secret to your spouse").

Appeal to Pity (Argumentum ad Misericordiam): using pity to get the listener to accept the argument ("I'm a valuable contributor to this organization and I deserve a salary increase – or I'll lose my house and my family.").

Appeal to the People (Argumentum ad Populum): using reasoning along the lines to "if you want to be accepted or included in a group, you should accept this argument" (think of beer ads with attractive/cool people).

Argument Against the Person (Argumentum ad Hominem): responding to an argument by attacking the person, not the argument ("What does she know about fair wages? She's never worked a day in her life.").

Appeal to Authority (Argumentum ad Verecundiam): citing an unqualified authority in support of an argument ("Even Harrison Ford has said that labor law needs to be reformed.").

Appeal to Ignorance (Argumentum ad Ignorantium): using an argument that begins with stating that we don't know anything about X with certainty and then concluding with a definite statement about X.

Accident: incorrectly applying a general rule to a specific situation.

Hasty Generalization (Converse Accident): inappropriately extending a conclusion from a small group (that is not representative) to a larger group ("That HR manager is incompetent therefore all HR managers are incompetent.").

False Cause: relying on a causal link that does not exist. Forms of this fallacy include concluding that event A causes event B because...i) event A precedes B, ii) event A and B are correlated (but actually event B is causing A), and iii) event A coincidentally happens at the same time as event B.

Missing the Point (Ignoratio Elenchi): concluding something other than what the argument logically implies ("The sick leave policy in this company doesn't provide a limit on the number of sick days and it is being abused by the employees. Therefore, we need to get rid of the union.").

Source
Patrick J. Hurley (1985) A Concise Introduction to Logic, Belmont, CA: Wadsworth Publishing.