I keep seeing inflammatory statements about members of some group where it's left deliberately unclear whether they mean some, most, or all members of the group.
For example, someone will tweet "Australians club baby penguins!" The intent is to encourage outrage against the malevolence of Australians. This is unjust (I guess), but if pressed the author will fall back on the defense that indeed more than one Australian is known to have bashed penguins and "that's all they meant".
To some extent they're exploiting a defect of the English language :-(.
An extension of this fallacy is to say "Xs Do Y and yet they do Z" where some Xs do Y and some Xs do Z and there is some inherent contradiction between Y and Z. This is designed to highlight dishonest or incoherent behaviour, but of course glosses over the possibility that the sets of Xs doing Y and Xs doing Z have small intersection. This is especially frustrating for members of X who do Y but not Z. Example: "Yesterday Australians liked cute animals, today Australians club baby penguins, WTF?"
Sure, these examples are ridiculous but real ones are everywhere. (I don't cite real examples because their content would distract from the point.)
Update A couple of people mentioned that this is a subcategory of motte-and-bailey behaviour. Actually I really like that Slate Star Codex blog. There's an article there that is quite similar to a theme I wrote about.