An excellent example is "Ancient Aliens"*. The show is wrong, to be sure, but very careful to make wrong implications with non-wrong claims. IMO it ought to be required viewing in all elementary schools.
https://www.gutenberg.org/files/48612/48612-h/48612-h.htm#Pa...
> Take the statement: "Harry said to me, he said, 'I never told anybody that Al's wife was a retired strip-teaser.' Mind you, I don't pretend to believe Harry, but that's what he said, all right." What are the possible true sources for the statement of fact or libel concerning Al's unnamed wife? What are the alternatives on ostensible sources? First use? Second use? The common sense needed to analyze this statement is of the same order as the process involved in analyzing the statement: "Reliable sources in Paris state that the visit of the American labor delegation has produced sensational repercussions in Moscow, and that Moscow, upon the basis of the American attitude, is determined to press for unification of the entire German labor movement."
* for those who have not seen it, each episode is a work of art, starting out with the uncontroversial, and ending with some wild hypothesis, with the "documentary format" hosts couching everything in impeccable language. A typical statement: "Ancient astronaut theorists believe X. What if it were true?"