Many decades ago a colleague of mine suggested that students in his logic class look in the letters to the editor section of the paper for examples of sloppy thinking. His advice still works.
It would take a textbook to cover all the errors in thinking. But read the letters critically, and you should have no trouble finding a treasure of sloppy reasoning.
A common error is identifying correlation with causation. If a state with the death penalty has a higher murder rate than a state that does not, some take this to mean that the death penalty has no or little deterrent effect. Maybe, but there could many causes that affect the murder rate in a given state besides the presence or absence of the death penalty.
Perhaps even more widespread is drawing too large a conclusion from too few facts, too big a generalization from too few particulars. If the first ten people you see entering a new town are white, you might conclude that the population is mostly white, whereas they might be the only whites in a village with twelve hundred blacks.
On and on it goes.
Thinking is hard work, and few of us do it well. Just take a look at tomorrow's newspaper.