As someone with more than a passing interest in the katana for the last 30 years and the good fortune to handle a bunch of period versions over the years I found his videos on them pretty poor. One of the poor things about youtube history videos are there are far too many where someone speaks for 5-20 minutes about a subject he knows little about. A friend brought a few over and I swung a couple isn't much in the way of research.
My knowledge on swords is very limited. I simply found it refreshing for someone to say that the Katana itself was not a heavenly sword created with ancient Japanese Magics. In truth this alligned with what I learned about the Gladius, it was simply a stabbing tool used by men who knew how to use it to maximum effect, the Roman Legionary. I admit that this is the limit of my knowledge. I am really interested in knowing what you found misleading about the video.
Well, everyone knows that the Katana is so totally awesome is can cut a femur in half floating in a stream or some such! I do appreciate the fact that we are starting to get penetration of the idea that a tachi or katana is simply a curved piece of steel with an edge; a few extremely well made, most Ok to really good, and a decent minority that were crap. I had a chance to handle some period European swords in the back at the Higgins armory and the steel was just as nice as many high end katana. This cult of the fancy giant dinner knife is best served dead! The fact that much of the reason Japanese steel has the mutli-layers and extensive forging is because their ore sucked so badly gets dismissed. On the scholarly side, I tend to believe the more recent research that says the steel in a good katana was not as good as that in a contemporary European one of similar quality. If I had to rely on one, modern off the shelf stock is better, stronger, and more pure. . . .
As to the video, stating tachi/katana are all roughly the same in design is as silly as discarding Oakshott's typology and saying all European Type Xii's through XVII's are all the same. There is a tremendous amount of variation in Japanese sword design, even during the Sengoku period. Not just length, but curvature, weight, width, handle design, handling, etc. One thing that often gets missed is that most of the swords which survived into the Edo period had to meet gov't regulations, so if you wanted to wear an old sword you had to chop it down to meet official rules. This leads to many early swords looking like Edo period ones because they'd been heavily mutilated. Again, it's like handling good European longswords. The construction is similar in them but the design noticeably varies according to the purpose. I suspect part of the problem as well as that Katana has come to mean sword (instead of a the more basic "ken") to we Westerners and so we arbitrarily dismiss all the weird and wonderful variations as some other hard to pronounce Japanese name.