I think you're glossing over something very important though - which is that he visibly demonstrated that he was wrong. I understand his intention and how he was building up towards the end, but this video makes me question everything he says rather than believe him. He is very much telling us to ignore what we saw with our eyes because it disagrees with his prediction, with very little explanation as to why. He made a prediction, he demonstrated for us that his prediction was wrong, and then he told us he was still right. If that's not an appeal to authority then I don't know what is.
I just don’t think it’s anywhere near as egregious as you make it sound. If he had literally told us to ignore our eyes, yes that would be bad. But he explicitly said that things were close, and that variations in the plank can cause slight differences, and that averaging a few trials would show extremely close results. Sure, you have to “take it on faith,” but it’s a very reasonable explanation, and by the end of the demonstration (when you see the much larger difference with the hollow cylinders) it becomes clear (or at least extremely easy to believe) that the tiny variations in earlier experiments were indeed the result of “impurities” in the physical medium rather than attempts to conceal inaccuracies in the physics claims being demonstrated.
I admittedly could be wrong, but I feel you're approaching this video from the assumption that he is a physics professor and what he says must make sense. I suspect you've already taken physics at some point and this reinforces what you've already learned.
Consider this from the perspective of someone who knows nothing of physics and is skeptical of science and academia. Here is a person that shows us he is wrong, does almost nothing to rectify this (there is a very brief explanation, but why not more demonstrations? Or really, why not just prepare a better demonstration that doesn't have these problems?), and then continues to pontificate as an authority figure.
If his goal is to offer a refresher to people that already know the physics, okay I guess this makes sense, but I sure as hell would've liked a refresher on the equations personally (so I am not the target demographic). If his goal is to teach people that know nothing of physics, he really could've done a lot more to actually teach and explain things.
Getting back to my first paragraph though, I feel like this comment thread might be a great example of humans being humans - everybody is susceptible to confirmation bias (again I could be wrong, but that hypothesis makes the most sense to me). If you didn't already understand the physics and you didn't take him at his word because he is a college professor, honestly his tutorial is unconvincing. He completely ignores the scientific method!
If this was a scientific experiment, then what you consider 'very reasonable explanation' I would call a lot of hand-waiving to explain away the difference between the theory and the experimental outcome.
He gets away with it because he doesn't need to convince his fellow scientists, only a bunch of pupils. But it is nevertheless quite unscientific.
