Good story Occam, and yes I think that playing and discovery are the natural ways to learn and school should have more of that, bring out the natural scientist in everyone. 
That’s why Good Math Videos are merely good and not excellent. Television is an old technology that shows videos, but videos are one-way there is no interaction its just the obsolete couch potato idea again. Instead, now-a-days, we have computers, these are the modern technology that allows interactive discovery and play, even if that potential has not been well utilized by commercial software. I do see some who agree with me who are offering to step forward with some good interactive “physics java applet” (just Google search that phrase to see many examples). Here’s some examples:
http://www.falstad.com/mathphysics.html
http://pdukes.phys.utb.edu/PhysApplets/appmenu.htm
That’s shows that the free software movement can do some things that the commercial software won’t really do. Java is just the language of choice in achedemia and science it seems, rather than Flash. So you’ll need the proper java plugins to use those.
Once the video becomes interactive then it could be called many things, like interactive animation, simulation, video game, virtual laboratory, etc. Video games are made with good physics simulations, the math really is in there, and if they’d show the audience some of the math then they could become educational, but no that hasn’t happened.
And to step from excellent interactive discovery up to great, one needs a customizable, self documenting, programmable interface to the interactive video. They need to offer a good interpreter so that the audience can recreate, customize, experiment, and expand the interactive video that they’re using. Books are good, as you said, but they just aren’t as dynamic and exciting as a computer can be, one can play a video game not just read it. 
Interactive tests where the test tells you when your answer is wrong, giving you some constructive or encouraging feedback immediately, and then giving you a chance to look-up and double-check your answers, this may sound like a very simple idea, but I’ve tried it and it is a very good learning technique. It can be scored as 95% or higher is passing. Astropitch is close to what I’m talking about, but has no feedback and unlimited retrys.
If Kahn has Gates’ money behind him, I hope he learns that video is the old has-been technology, and dynamic interaction that is customizable is the modern way. With Gates’ money, there is no reason that modern learning tools can’t be made into a Flash, Java Applet, Javascript, widget for a web browser, desktop application, or cell phone app. I hope that Kahn gets that idea and stops putting so much energy into the one-way videos. But did you hear him say that he wants to use his video to free up the teacher’s time for more face-to-face interaction? Isn’t that ironic, computers providing more time for in-person human interaction! Its ironic, but no surprise that bringing automation home can do that.
Long term memory is another big issue that needs better techniques for proper learning.
Reviewing and teaching yourself the math that you missed, for whatever reason you missed it, is a great idea. Why waste an education? Math texts have changed, you can find one written in a style that YOU like, now-a-days. When a student asks a question, they should expect that the teacher try to answer it for them in a way that the student understands. 
