I'm liking the basic idea of the skill system (sympathies for those that don't), but I think we're still lacking some key information.
Bonuses to skills aren't necessarily numerical bonuses, although they can be. If I've read the transcript correctly, for example, double-training Stealth let a character move their full speed while hiding. In fact, non-numerical bonuses are better than numerical ones when they permit you to do things without a roll that others would need a roll to do or couldn't attempt in the first place. This makes sense with the emphasis on whether one should even require a roll in the first place. That could be decided by the raw ability score, but it can also be decided by training. Rather like a more flexible version of skill tricks from 3.5's Complete Scoundrel. Those sorts of value-added options could also keep the disparity in skill check bonuses between characters within a reasonable range. I'll be interested to see how high bonuses are allowed to go. The variance of the d20 is quite large, so trusting a bonus to reliably show competence vs. another character usually requires a fairly large bonus, and with it all heaps of trouble. That's a good reason to take skill training in a less numerically oriented direction.
In my homebrew game we name our own skills, each of which contains 3 basic proficiencies. (For example, my character has the "Rough History" skill which for him encompasses Begging, Urban Survival, and Weaponry plus anything else that makes sense with the backstory. He also has "Cleric of Bahamut", which covers First Aid, Leadership, and Theology and anything else relevant to that part of the character. It also means his knowledge of theology, for example, is limited to what a cleric of Bahamut would have reason to know). However, the main effect of training these skills is to allow for more reliable (if limited) success without greatly increasing one's maximum potential, while the main affect of larger ability scores is the opposite. (This is success-based dice pool system, so it comes directly from the math.) These skills apply to any check using any ability score that can be justified. When the connection is tenuous, the DM can choose to grant half the bonus. In our homebrew a creature of average human dexterity with 2 ranks of training is basically on par with someone with superhuman natural ability (ability scores 10 and 20 in D&D terms), but the trained character achieves the average result much more reliably. I think similar characteristics could be achieved in D&D Next by making skill training less about a +n bonus, and more about what training lets a person achieve apart from or in addition to a check.