This fallacy underlies a lot of denialist propaganda. The mistake itself is pretty easy to understand: take some actual feature (typically a scientific error, or an anomaly that is difficult to account for) and make it seem like it decisively proves that a whole body of knowledge is mistaken.
One way that this fallacy manifests itself is in conspiracy theories. People who are suspicious of a government cover-up of a faked moon-landing, or the assassination of JFK, or the destruction of the Twin Towers, will often examine available photos, video, and reports in great detail. And their detailed examination will often reveal many curiosities that seem hard to explain.
The shadows of the astronauts on the “moon” point in different directions, even though the only light source is the sun; the bullet holes don’t line up with the location Oswald supposedly fired from; the skyscrapers collapsed in a way indicative of a controlled detonation, and so on.
At least some of the supposed “inconsistencies” are due merely to the fact that we are paying far more attention to the details of a particular scene than we normally do. Anything viewed in extreme close-up will look unfamiliar, simply because we usually don’t pay attention to that level of detail. There are “anomalies” everywhere, but we almost never notice them because they’re small, fleeting, and irrelevant.
A second, very important, manifestation of this fallacy is in denialist critiques of consensus science. Climate change deniers, for example, will trumpet any false prediction made by the IPCC (or any example of unpleasant politics of science that comes to light) as a decisive refutation of the entire IPCC process. But this is making a mountain out of a molehill. Finding one example of sloppy editing allowing in misguided prediction in no way implies that the rest of the 99.9% of the report is equally mistaken.
We need to have a reasonable perspective of what the overall body of scientific knowledge is before we can decide that some particular fact is decisive. If we have thousands of examples of transitional fossils, then the fact that Piltdown Man was a hoax shouldn’t shake our confidence in the science of evolution.
The problem is, many people in the general public don’t have this large-scale perspective. So when denialists present them with a seemingly large list of “problem cases,” they conclude that the entire scientific field is rotten to the core. But this conclusion is based on ignorance. And mistaking a molehill for a mountain is our fallacy of the day.