We have all seen it...but usually only mathematics teachers stop and worry about it. I am talking about the making of mathematical errors in public. That is, the old 0.99 cents syndrome exemplified.
In turn, you may be looking for good examples of these mathematical errors by advertisers, the media, reporters, politicians, and the non-math public. Believe it or not, Paul Cox has done that for you...at his web site Math Mistakes.
First, he provides a Glossary of Mathematical Mistakes. By citing specific examples and descriptive titles, Cox illustrates re-occurring errors such as factoritis, ratiocinitis, recursive arguments, circular reasoning, the Law of Zero Return, division errors, sample trashing, and dramadigits. A wealth of teaching ideas!
Then, Cox provides a lengthy Archive of mathematical mistakes, such as the "Top 5 Math Mistakes of 2003," "Art by the Numbers is Mediocrity," and "Lottery Math." You might share them with students to see if they can find the mathematics errors.
Finally, Cox provides responses from readers of his web site. These responses include additional examples...by this point one becomes depressed at the lack of mathematical literacy in this world!
Though not connected to the theme of his site, Cox also provides a collection of some mathematical problems (perhaps trying to promote problem solving as a way to overcome error-tendencies) and numerous mathematics links that will provide several afternoons of exploring.