Responses bolded in quote for laziness :-)
It's so much easier to respond to comments on your own work than examine the work of others in detail...So, this is more or or less stream of consciousness notes, the first thing that comes to mind when reading this thread. I'll go over to the Wiki later.
I appreciate the offer, but I won't hold you to it. It might be that this fails the "would you play it" question at the start, in which case I appreciate your taking a look at it but wouldn't ask for anything more.
No skill points based on intelligence is a really new approach to me, and not one I've ever seen before. My first instinct is to cling to the fluff and say "But smart people learn more!" but we'll see where this goes. Your reasoning seems basically solid.
An interesting side effect of that is that intelligence is now a "useless" attribute. It is, together with Charisma, the only attribute that doesn't seem to influence anything other than skill modifiers, outside of classes. Strength has breaking down doors and carrying capacity. Dexterity is AC and reflexes. Constitution is HP and fortitude and Wisdom is will saves. Pure int and cha are... nothing. That said, the replacement save thing might save this.
It's mentioned above, but there's a suggestion in the full work to migrate Fort -> Str, Ref -> Int, and Will -> Cha in conjunction with the standard assignments being represented in skill format. If you don't like that suggestion, and I know plenty of people who don't, then I get to lean on people caring about skill abilities to not dump attributes. In playtesting (my groups and others), this is exactly what they've done.
Cross class ranks: I think most house rule collections I've seen do this now. It just makes sense.
Retraining: this is something I never liked. "Oh, no. Redgar can't climb anymore. He learned swimming this morning." It's... silly. Yes, I see the benefit of flexibility. And I dislike it.
I haven't actually seen people retrain in playtesting, so I think most people just don't worry about it. So it's mostly an unrealized benefit, but one I wanted to make sure was available.
All boni are competence boni: why? I'd at least leave circumstance boni in. They make sense. A task is easier for some reason, so you have a +2. It's one of the DMs most important tools for players with creative planning.
That was not an intended casualty actually. "The DM's best friend" +/-2 modifier should be in there still.
Skills unlock new abilities: no problems with that. Good thing. At least you didn't include Skill tricks, I hate them.
Degrees of success are theoretically a good idea. I'm just wondering how complicated this system is now getting. Have you ever seen it in actual play?
Yes, and gotten playtest reports. There's some extra lookup at the table involved, but everyone who has tried it has been fine with the slight delay in lookup given the other things that came along with it (and there's arguably less slowdown in other places that makes up for it anyway).
I'm not sure I like the "Taking 20 includes having rolled a 1" rule. Taking twenty usually represents being much, much more careful. I don't see "automatic failure first" working with this. "I'm taking this trap apart part by part with my finest tool and the plans open on my lap so nothing can go wrong!" -> Bang automatic failure, you die. This just doesn't seem right. Taking 20 is to avoid failures, not producing them.
The taking 20 rule also normally doesn't allow you to do it in a lot of situations. It's a mechanical representation of rolling over and over again until you get a 20, which often involves rolling very low first. This is just a different form of the rule so that I don't have to include "yes take 20" / "no take 20" on abilities. Instead I can just say "you can take 20 whenever you want, but it might not work out".
Knowledge skills. This, I think, is the first change that makes me go "nononono" in my head. That would never happen at my table. Knowledge skills are essential to the game. I don't want them handwaved. You say they depend on the type of campaign. So does every other skill. If you never need to know history, knowledge: history is useless. If you never get punched while spellcasting, concentration is just as useless. If we exclude every skill that could ever be useless, there would be nothing left.
Also perform. It's an essential skill, and I wouldn't want it removed. Half my characters are either bards or practised performers, and I can think of a dozen anecdotes off-hand where a player's performance saved a campaign in some way. Same with knowledge. Walking on air comes up very rarely. Where it does, I'd probably just allow a player to do it for show (i.e. write it on their character sheet).
The intent here isn't to exclude skills that could be useless (climb and swim are still in after all), but to exclude skills that don't scale like the others so that you don't spend character power on character fluff. When you get to specific skill examples, I hope it's more obvious what the differences between them are. I am working on more concrete methods of breaking these things down, because people want to play master flutists and smiths and sages and don't want to just write it in their backgrounds, but the skill point method is basically a non-starter with everything else.
As for the idea that air-walking comes up rarely, I really don't know how to respond. Flight comes up all the time in my games, much more often than performances, and since air walk is just another form of that it too comes up all the time. And I'd rather codify that sort of thing in the advancement rules than hope that nice DMs (like you apparently) would just let people write it on their sheet a certain point.
I'll get to specific skill examples later.