I want to come back to this.
When I first watched the Bill Maher clip, I was not trying to estimate the probability that the examples he gave were faithfully represented rather than misleading. I didn't feel like it was my job to fact-check Maher so much as just to understand his point, and his point didn't really depend on the specific facts involved. I assumed without thinking about it that his facts were probably right, but even if they weren't, other facts could be substituted in to make the same point.
It occurs to me that I was doing exactly what I find frustrating when others do it. I know some people who watch Fox News and get outraged about how "the left" is so outrageous because of this cherry-picked example or that one, and they are completely oblivious to fringe nature of those cherry-picked examples, or of numerous examples of people on the right being equally or more outrageous. "First, stop looking to be outraged," I think to myself as I silently criticize them, "and second, if you're going to be outraged, at least get your facts right."
The Bill Maher clip that I linked to was selling outrage. I saw it as righteous outrage because he was criticizing sentiments that I deemed worthy of criticism. So I didn't bother with fact-checking because the specific facts were incidental -- it was the truthiness of the general attitude that mattered. That is to say, I had basically become the Bill Maher-watching version of a Fox News-watcher that I normally find discreditable.
There are a number of lessons I might learn from this, but here's one that I think is pretty good.
New Rule: Don't be outraged by stuff leftists have done if I've heard about it only from people on the right; and likewise, don't be outraged by stuff people on the right have done if I've heard about only from people on the left. Wait until I come across outrageous stuff organically before getting into my mode of condemnation. (I'm saying "left" and "right" here as a simplification, but it's more complicated. Maher might lean left as a general matter, but when he criticizes political correctness, he's not really criticizing people on his own side. He's criticizing his opponents regardless of where they fit on a vague left-right pseudo-continuum.)