I thought this was rules that actually needed fixing? The skill system is not broken, or at least not broken enough that any of the above fixes and tweaks could be called anything but personal preference.
Here's my top 10 + 1 bonus
1) Barbarian needs too lose its alignment restriction and its culture and setting specific flavor, to become the 'Fanatic'.
2) Paladin needs to lose its alignment restriction become a 'Champion' class similar to Book of the Righteous's 'Holy Warrior'.
3) The craft skill mechanic is not in the slightest logical as written, producing utterly random results. A more detailed system needs to be developed.
4) The rules for damaging objects are underwritten as they are (alot of hand waving) and produce highly illogical results in the hands of all but an experienced DM. Resistances of objects to particular forms of attack should be explicitly outlined, and hardnesses should scale up with thickness just as hitpoints do (this explains for example why a tank's armor can be impervious to any number of .308 bullets, why you can break a thin wooden board with one hit of your bare hands but a thicker one will beat your hands bloody long before it would break, and why six inch thick glass can take a heavy hit without even cracking).
5) The profession skill is vastly underdescribed and needs at least several pages of fleshing out explaining what it does plus a side bar on profession status that explains the optional mechanics which allow (for example) stewards, lawyers, engineers and physicians to generally make more than beggars, porters, chambermaids, and stevedoers.
6) The 3.5 weapon sized rules are semi-realistic for no good purpose, and need to go back to the more abstract 3.0 rules (which I figure most people use anyway).
7) All classes need access to the profession skill, as its potentially the broadest skill in the game but unlikely to be overpowering and its very difficult to explain how a fighter has acess to ride but not for example profession (boater). (I'm semi-inclined to give all the classes with 2 skill points per level, 3 per level, but I'm afraid of making Int even more of dump stat in cleric and fighter, and in any event thats a tweak and not a fix. The 2 skill points/level rules work fine and are logical as is.)
8) The rules as written prevent a running player from tackling another one unless the tackling player has 'improved overrun'. I'm pretty sure I don't have the 'improved overrun' feat, but I can tackle an opponent while running. This is a major oversite which has implications fairly often in chase sequences.
9) The rules for long duration movement are very rough and far from ideal. Persumably extended running and extended hustling should require saving throws just like a forced march. The incorporation of a refined version of the 'Hot Pursuit' rules into the core rules would also be a major and important addition, though technically that is an extension and not a fix.
10) For versimiltude, animal intelligences should be allowed to range higher to reflect the true range of animal ability (for example, lizard: 1, mouse: 2, cat: 3, dog: 4, ape: 5). All most animals are more skillful than presented, and compared to humans have certain advantages do to differences in body plan not represented in the rules. For example, all dogs should have Endurance and Run as bonus feats (the rules as written allow many humans to run faster than dogs, when in fact humans barely can keep up with even tiny dogs).
11) Realisticly, the constitution of most things in the game is too high, especially for small or smaller creatures. Reading the rules one gets the impression that Humans are one of the least healthy and enduring creatures in existence, rather than in fact one of the most (cats for example have pretty fragile constitutions). Still I don't count this among my 10 real fixes, because realism is not a particularly good justification on its own and achieving a target number of hit points for a particular CR is probably a better reason than realism.
In addition to those fixes, I'd say the most glaring deficiency in the rules is the absence of a general broad price list that makes any kind of economic sense whatsoever (beyond building a character at 1st level).
My number one tweak is that there are a number of divinations, detect evil, detect lie, know alignment and so forth which are too gross in thier application and need rules for resisting them through the mundane means and not just obscure magic. Simply put, you ought to be able to bluff your way out of them and fake your alignment in the same sort of fashion alignment is faked in Use Magic Device. So for example, rather than detecting a lie outright, discern lies might give you a +20 bonus to sense motive, and detect evil might require one or more opposed checks of some sort if the source is a sentient being.