If Samuel Johnson were alive today, he might well decide that the very last refuge of the scoundrel is statistics. I will briefly mention three of the most serious sins committed here, and point you toward the articles that do an excellent job of explaining the issues in non-technical terms. Probably the most egregious crime is the constant confusion of correlation with causation. Correlation simply means that a connection exists between two sets of data. For example, there is generally a correlation between height and shoe size.
Taller people tend to have larger feet than shorter people.
The fact that a correlation exists, tells you nothing about cause and effect. A correlation between A and B might be due to A causing B, B causing A, C causing both A and B, sheer coincidence, or experimental error. Yet over and over again correlation is treated as cause. See Kamin on this point, too. Here's how they work.