I've joined physicsforums because I would like to understand QM in the sense meant in the topic header. Thus I've been discussing Bell's Theorem and related issues with the experts here; and obviously none of them thinks that watching a video or reading a Wikipedia article (which they may have written) will make one understand it, in that sense (funny lecture though, makes me think of Woody Allen). Which brings me to the next point:
OK then, like him I now also claim that no one understands QM. And you may quote me on that, pretending that I only meant to illustrate the idea that the quantum world, at first glance, seems very different qualitatively than the world we live in at the scales that we perceive things. However, I did not say that nor suggest that, and neither did Feynman. What I mean is very different from that, as a matter of fact it is closer to what you suggest next:
Well, that is generally what "why" questions and the word "understand" mean - as also already discussed in this thread and numerous other threads.
Then you may not be able to understand why Feynman and many other experts agree that QM is not understood.

As you realized, he knew perfectly well how to mathematically describe and apply QM - he even excelled in it. We all know that that is
not the sense in which QM is said to be "not understood". And in what sense it is meant, has been elaborated already by others in this thread.
That would be unachievable. However:
The problem that we are discussing here, is that we even lack a plausible model of how and why QM works. To quote Feynman also on that one:
"The more you see how strangely Nature behaves, the harder it is to make a model that explains how even the simplest phenomena actually work. So theoretical physics has given up on that."
It is in that sense that QM is "not understood" - as many people have tried to explain now (see for example posts #2, 16, 74, 78, 79).
PS: I think that in what way QM is "not understood" has been sufficiently explained by now.