The Five Common Thinking Errors, as pointed out by the Book of Readings are, Non Sequiturs, False and vague premises, Ad Hominum, Begging the Question, and Red Herrings.

False and Vague Premises are cases in which the conclusion follows the premises logically, but the premises aren't true, leading to a false conclusion. A modern example is

1)Democrats Believe in abortion
2) George W. Bush is a Democrat
Conclusion) George Bush Believes in Abortion.

Ad Hominum is an aguement which goes against a person rather than that persons beliefs. Rather than argueing with someones beliefs you are personally attacking the person. An example would be

1) Oakland fans say Tom Brady funbled the ball on the play which led to the tuck rule.
2) Oakland fans are wrong, it was an incomplete pass
Conclusion) Oakland fans are wrong because they smell bad and don't know anything about sports.

Begging the question is an example of an arguement in which you make a statement proving somehting is true, where you already assumed it was true. An example of begging the question is

Bilbo Baggins: Thee are't any orcs in the mountain because the dragon Smaug is there.
Gandalf: How do you know Smaug is there?
Bilbo Baggins: Because there aren't any orcs.

Red Herrings are tools used when losing an arguement to chane the subject or distract everyone from the real topicof discussion. A good example of this comes from the Book "Animal Farm"

The leader is a pig named Snowball meant to depict Stalin. Whenever the other animals complained about the lack of food and haing too much work, he simply told them it was better than it really was, and in time they will be rich. This tactic worked until the other animals realized the work was getting harder and harder and they eventually killed snowball.