Admit it, you don't want to hear about it. And that's just what they're counting on. 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.