One of the primary assertions in the video of why diet soda is bad for the "acid-alkaline" balance is the presence of phosphoric acid. He goes on to claim that because phosphoric acid is close to battery acid in its pH it leaches minerals from bones and other organs causing sickness.
As an aside I should make a video and put on youtube, with cute hand gestures and quasi official sounding commentary, and say that phosphoric acid is alkaline forming, that should terminate this debate. Why won't it, oh I guess my hands are not as knowledgeable as this guys hands are, sorry!
Anyway back to the assertion that phosphoric acid leaches minerals from the body, there is very little proof of that.
http://en.wikipedia.org/wiki/Phosphoric_acid The section on "Biological effects on bone calcium and kidney health" states there have been very contradictory results from studies performed on phosphoric acid intake vs. mineral leaching, but the general medical consensus is that phosphoric acid does not leach minerals from the body.
Now I am not recommending drinking 4 gallons of diet pop everyday, that is foolish, but so is asserting that our body is that fragile that we have now control the pH of our food. Our bodies are the result of millions of years of evolution which has survived diets of pure vegetable, pure meat, massive amounts of fat, give it a bit of credit.