"They say banning smoking indoors saves thousands of lives but what about the hundred thousand dead by bombing in Fallujah?"
CAUSE AND EFFECT MISMATCH
This technique confuses the audience about what is really cause and effect. In fact, the causes of most phenomena are complex, and it is misleading to say just one of the following: "Tuberculosis is caused by bacteria", "Tuberculosis is caused by unregulated capitalism that creates poor working conditions", "Tuberculosis is caused by a lack of effective antibiotics".
WEAK INFERENCE (or False Cause)
The weak inference is when a judgment is made with insufficient evidence, or that the conclusion does not necessarily follow from the evidence given. For example, ducks and geese migrate south for the winter, therefore all waterfowl migrate south for the winter. Or, most rich folks vote republican, therefore most people who vote republican are rich.
This is when a comparison is carried too far. Example: "The economy is following the same path as right before the great depression, therefore we will experience a stock market crash soon!" SLIPPERY SLOPE would be an example of a faulty analogy. The slippery slope makes the argument that a shift in one direction will continue to lead to extremes (ex. smoking pot will lead to heroin addiction). It is not necessarily so.
Take an accurate quote from a particular target but cut off the quote - partial or out of context - so it can be used to substantiate propaganda whose agenda is either to amplify negativity against or undermine the target. Example: "Comedian Louis CK tells an Israeli audience he'd rather be in Auschwitz than New York City" suggests the comedian is belligerent, insensitive crass and opposing the audience. But in the full quote, the word "now" is appended, i.e. Auschwitz today is a museum not a concentration camp, whereas New York City is a difficult environment for the comic to speak freely. The audience was paying to see Louis CK and it turns out the quote was part of a general banter the audience found it hilarious.