A lot of things here don't work like the old skill system. Here's a list, along with some discussion as to why:
1) Characters no longer gain or lose skill points based on their intelligence modifier.
The skills are really substantially stronger. Giving bonus skill points for any attribute is more like giving bonus feats for having a high attribute, or giving bonus spells to everyone for having a high attribute. It basically makes that attribute too valuable in comparison to the others. If you feel that this makes intelligence less valuable, I would agree with you to a point. It's no more or less valuable than Wisdom or Charisma are for any given class (excepting save considerations... more on those later), as Int is the relevant attribute for the same number of skills and other bonus changes mean that you need a decent one if you want to be good at those things. You can only really get away with dumping Int if you're not playing a character with Int based skills that you care about, which seems sufficiently in genre to me. There is also a related save variant due to some "secondary save" style skill abilities that shifts the reflex save burden to Int that helps a bit.
2) Cross class skill ranks are purchased at the cost of 1 skill point, not 2. The cross class maximum skill rank is equal to your (character level + 3), divided by 2. This is rounded up.
I'm comfortable with a trade of 1 level appropriate skill for 2 sets of not-level appropriate skill abilities, and I don't see any reason to charge people any more than the loss of power for the increase in flexibility. I think it's a fairly poor tradeoff most of the time anyway, but there are reasons someone might want to do it. Why this is a poor trade will make more sense in a few points.
The rounding rule is specifically so that people don't have skill points laying around after level up, since they can't otherwise invest in their cross class skills every other level.
3) Retraining is a core part of this revision, not an optional rule.
This gets some flack from people for a number of assorted reasons, but is more or less required if you want to approach the level of flexibility full casters have. They get to prepare different spells from your pool, you get to prepare different skills from your class list given sufficient time. Additionally, the class skill / skill point assignments are set in such a way that there aren't enough class skills for people to retrain without some overlap with their previous skills. Further, selection of any skill feat is going to provide a strong incentive to not retrain certain skills, so the narrative complaint that "you've always been able to do X and now you can't" is somewhat mollified.
4) All skill bonuses other than attribute bonuses are now of the competence type, and capped at +3. This includes racial bonuses.
4a) Synergy bonuses no longer exist.
4b) Skill items are drastically different, and grant non-stacking ranks or re-rolls instead of bonuses most of the time.
4c) Spells that grant skill bonuses or ranks need to be toned down, removed, or rewritten to not interact with the skill system in the first place.
This is a design decision stemming from the following problem: you can't set DCs without an expectations of what bonuses people will have at a given level. If you allow people to have substantial bonuses to skills that they already have maximum ranks in, you get to decide if those bonuses can make people auto-succeed all the time or if those bonuses are required to have a level appropriate modifier in the first place. Since the first is unacceptable and the second is an item tax, I don't want to do either of those. So skill bonuses got removed or retooled to keep people's bonuses more in line. They might have substantially less than that, but they won't have more. Attribute bonuses remain somewhat problematic, and there's a discussion about the options you have for dealing with them.
5) Skills unlock new abilities when you put new ranks in them.
This is sort of a mechanical kludge to deal with the RNG. If you want low level characters to not attempt high level skill abilities, you have to spread the DCs out a lot or put up other barriers to entry. Spreading out the DCs has other issues associated with it, so barriers to entry it was.
6) Skills include benefits and penalties based on the degree of success.
This is designed to keep skill abilities relevant as you grow in level, and also to incorporate the "take a penalty to your roll to try to do better" thing.
7) "Taking X" rules have been updated.
You can take 4 times as long to "take 15", which was added to fill in the results gap and because there is a margin of success every 5 points. Jumping from bare success to fantastic success with no way to hit the middle was odd.
"Taking 20" includes a rule that you are considered to have rolled a 1 before you roll the 20, so any possible failure will happen. This serves to basically reserve taking 20 for times when there is no chance of failure you care about without actually putting the prohibition in, because the prohibition is weird in some cases with the measured success setup.
Additionally, you can "take X" even under pressure as long as you have 4 more ranks than the required amount. This rule is there to allow people to just do things without a chance of failure, since anything you could attempt 4 levels ago should be something you're comfortable with now. You will still check when you want to try to do better of course, but if "good enough" is fine for the situation you should be able to just do that. Ability check bloat is a serious concern for me with this revision.
8) Knowledge skills have been reworked, and aren't really knowledge skills anymore except with respect to monster knowledge.
The "know campaign" stuff ability was more or less valuable depending on the type of game, but also didn't really scale with level in any way that was good. So rather than make people spend character resources on it, it gets sort of handwaved now.
9) Craft, profession, and perform have been removed.
These skills just don't have the same utility value as other skills, and I don't really think it's possible to design them such that they ever would (well, you could do perform, but you'd probably invalidate the bard). If I told you you could walk on air or be a really really good bartender/flutist/mundane blacksmith, which would you choose? The standard handling of these is similar to knowing stuff, you write it into your backstory instead of spending character resources on it. There's a potentially more crunchy setup for this in my pile of WiP, but it wouldn't work on skill points at all.
10) Assorted subsystems and class features have been updated to better interact with skills.
Specifically riding, animal training, spellcasting interruption, overland movement, pickpocketing, tracking, trapfinding, and divine spellcasting. There's a whole chapter on it.