Not so much a list of things that need fixing, but rather things that I would change given the chance:
Remove almost all effects that change a creature's basic stats. This includes the level-based stat increase, the various items that give a +2/4/6 to a stat, spells like Bull's Strength, and so on. I would leave the ability of Wish to increase a stat as-is, and the equivalent magic books, but everything else would be gone. I would probably also keep ability damage, except that as with hit point damage it wouldn't have any actual effect until a stat reached 0 (at which characters would die).
Re-balance the stats. Mostly, Charisma doesn't do enough.
Remove most of the elements from the racial packages, particularly trivial bonuses that apply at 1st level but rapidly become worthless. Each race would have two or three reasonably significant racial features that set them apart from other races. (Weapon Familiarity would be gone. I hate that rule.)
More flexibility in several of the classes. I like the "d20 Modern" talent trees; I would be using these for the Rogue, Ranger and Paladin, amongst others.
Remove all cure spells from the Cleric spell list. Leave the Healing domain as-is. And re-design the Bard so that instead of being a pseudo-Rogue, it acts more like a Cleric-replacement.
Something needs to be done with multiclass spellcasters. The fix I have in mind would make the game "not D&D", though.
Give all classes either 3, 5 or 7 skill points per level. Classes that currently gain 2 would gain 3 (except the Sorcerer), classes that get 8 would get 7, and the rest would get 5.
Likewise, give all classes either 3, 5 or 7 hit points per level (d4 -> 3, d10+ ->7, other -> 5). Barbarians gain the Improved Toughness feat for free. Introduce a "hit point advance" rule that gives characters triple hit points at 1st level, but thereafter they don't gain further hit points until their 'real' total would be higher than the advance total (for all single-class characters, that would be at 4th level).
Hit points are split into two pools, the Quick pool and the Dead pool. When characters have a chance to rest after an encounter, theyrefresh their Quick pool to full. The Dead pool only refreshes with an extended (long-term) rest - at the end of the adventure, effectively. Magic healing, however, applies to the Dead pool first - this is why the Cleric loses all those cure spells.
Consolidate a lot of skills. Listen/Spot become Perception, Balance/Tumble become Acrobatics, Climb/Jump/Run/Swim become Athletics, Spellcraft rolls into Knowledge(arcana), and so on. Craft, Perform and Profession each become a single skill - it's not realistic, but it's hardly game-breaking. (I'd probably also rename the various Knowledge skills to just Streetwise, Arcana, and so on.)
Lower all fixed skill DCs by 3. Drop the 'quadruple skill points at 1st level' rule, and allow a max skill ranks equal to the character level. Drop class skills, synergy bonuses, trained and untrained skills, and the Trapfinding, Track and Stonecutting special cases.
Re-balance melee, thrown and projectile weapons. Basically, the damage done by an attack should be inversely proportional to the effective range of the attack. To that end, strength longbows should go. Stacking of magic bows and magic arrows (be it of the plusses, or more likely the flaming bow with shock arrows) needs to go. And there need to be 'bracers of throwing' or the like, that basically make any thrown weapon magical, as bows do for arrows.
Heavily reduce the number of 'named' bonus types. I reckon seven names is about the right number; everything else either becomes an unnamed bonus or is dropped entirely. As the types of bonuses is reduced, the magnitude of bonuses can be increased - a single +5 is equivalent to five +1 bonuses, but it probably feels better to be wearing plate mail of the gods than to be wearing a magic hat, boots, amulet, ring and bracers that do the same thing.
Replace the raft of existing combat options and subsystems with a fairly detailed stunt system. Basically, a character leanrs various 'stunt components' through his choice of skills and feats. He then describes his stunt and the DM determines which components would be required. If the character meets the prerequisites, the player makes a 'stunt roll' to determine success or failure, and the game proceeds. A bonus would apply to the first use of any given stunt in the campaign, the magnitude being determined by the DM based on his chosen style of game. (Ideally, the game should be designed such that a character can be designed to be dull-but-effective (Gimli), or effective-through-panache (Legolas), allowing players a choice of approaches.)
Rebalance the spells (yet again). The change to hold person to give a save every round is a not bad start, but it needs to be carried throughout the whole system. And something has to be done with the multitude of all-or-nothing save-or-die spells. Basically, we need a magical analogue to hit points, such that a failed dominate isn't just wasted effort, and a failed save vs finger of death doesn't prevent you from having fun for the hours until your buddies get you resurrected.
Speaking of resurrection, I would take steps to make character death, especially at high levels, less common, but also to make returning from the dead much rarer. Ideally, it would be the subject of a quest, but I can see how that wouldn't be ideal for the player of the dead character.
I would be strongly tempted to switch to 20 levels of spells, or however many PC levels there are in the game.
Remove XP as a spendable resource. Energy drain would need to do something else, item crafting will need to drain some other resource, and so forth, but that can be done. I would also disassociate XP gained with CR, and instead encourage DMs to mostly just wing it.
As with spells, the various magic items would need re-balanced. I think the fundamentals of what 3e does are actually fine, but there is some work needed.
Likewise, the fundamentals behind monster design are mostly okay, I think, but there are some holes. I think I would drop hit dice in favour of fixed numbers of hit points per 'level'. Then give Giants 14 hit points per level, rather than a d8 hit dice (this should get rid of their absurd BAB and saves, no?). Undead need many more hit points, or should apply their Cha modifier in place of Con (or both).
Spread out the so-called "low-level humanoids" across more of the level range. And change dragons to be a 'template lite' - we don't need 300 different dragons, each with 12 age categories, each marginally different from the next, and none of them easy to run from the Monster Manual - 20 really solid dragon stats would do us a whole lot more good.
Not really a rules change, but I would definately adopt the MM4 approach of providing a bunch of different examples of stats for all of the staple monster races (Orcs, Kobolds, Lizardmen...). Those things are really useful.
There's more, but some of the more radical changes would definately take the game to a "not D&D anymore" place (mana-based per-encounter spellcasting, for one), while others I think I would wait until my next edition to implement (separating the 'dodge' and 'ablative' components of AC, for example).
For the record, my list of things that actually need fixing is rather shorter:
1) Multi-class spellcasters
2) Level-adjustment races
3) Prep time is too long
IMO, any new edition (including Pathfinder) needs to fix, or at least signficantly improve, all three of these. Or, as 4e appears to do, it could change the game so significantly that existing issues are moot.
