What's wrong with 3.x skills? Yeah, there were a few hiccups at first:
Use Rope
Hide + Move Silent
Balance + Tumble
Listen + Spot
But those were fixed in later games, like Pathfinder or True 20.
I'll use one example that's easier to explain, but with a note that if you start to dig, you'll find this same kind of problem in almost every 3E/3.5 skill.
Listen + Spot is supposed to fix a real problem. The problem is that a single Perception skill is way too valuable compared to other skills. You can get around that somewhat by rarely calling for skill checks (i.e. player skill matters when they say they look somewhere), though that is swimming upstream against what the rest of the system is pushing. You can try to buff out the rough edges with class skills, fiddly ranks, etc. to force people to take something else. Sound familiar?
Just because the initial 3E fix was worse than the problem in some ways, that doesn't remove the problem that was there. The 3.5 solution is half correct. It removes a "cure" that is worse than the disease. Then it kind of scrapes by ignoring the real issue, hoping no one notices with the zillion fiddly changes throughout.
To actually fix the problem, you have to do what Vision Storm said in the post below yours. Which is hard, thoughtful design work, with payoffs that aren't obvious until you've done most of it. Oh, and doing it will almost assuredly send a herd of sacred cows trampling over a garden, through a house, and ripping up a vineyard before they finally plummet over a ravine where the survivors drown in a raging torrent.
Thus the conclusion that some of us have come to that there are really only two reasonable courses of action, given that in the "hard, thoughtful design work" area, WotC seems to be rather limited, and to running off the people that tried: Ignore the warts and enjoy it for what it is. Or if that isn't possible any longer, give it up as a lost cause.
I'm not trying to convince so much as explain. When some of us say that 3E/3.5 isn't fixable, we don't mean there's no conceivable route to fix it. We mean practically, it won't happen, and if it did, many of its current fans wouldn't recognize it. Note that 4E and 5E both tangled with some of the hard core issues in 3E/3.5, with some success. They both also handled some hard core issues by writing them effectively out of the game entirely, to more or less success depending on who you ask, and their preferences.
I don't have the slightest doubt in my mind that both Chris's suggestion for using non-core classes or Tenbones's suggest to get Fantasy Craft are great options, if they happen to appeal. That is, I'm fairly certain, despite having never even read either, that they are both more coherent than 3E/3.5 as a system at the table. They are also going to be a bit more narrow in appeal, as any well-designed fix will be.
I guess it depends on the specific instance of 3.x.
D&D 3.5: Search, Listen, Spot
D20 Modern: Search, Listen, Spot
Spycraft: Search, Listen, Spot
FantasyCraft:Search, Listen, Spot
True 20: Search and Notice (This is the ideal arrangement for me.)
Mutants and Masterminds 2E: Search and Notice
Pathfinder: Perception
SW Saga: Perception
Mutants and Masterminds 3E: Perception
I've arranged the games (roughly) chronologically. The idea of a unified Perception started around 2007, and persists to this day, but I don't think it's fair to say that is a universal 3.x problem. There's too much variation in the sample set. I do think it's on target to say it's a problem for 5E, however.
Here's the True 20 skill array. I don't see any glaring problems here. I'd delete Concentration, and Escape Artist never seemed to be useful in our games, but other than that it's pretty solid.
Acrobatics
Bluff
Climb
Computers
Concentration
Craft*
Diplomacy
Disable Device
Disguise
Drive
Escape Artist
Gather Information
Handle Animal
Intimidate
Jump
Knowledge*
Language
Medicine
Notice
Perform*
Pilot
Ride
Search
Sense Motive
Sleight of Hand
Stealth
Survival
Swim
No one said that it was a universal problem with all 3e derived games in general, but with D&D 3e, which is the core rule set being discussed. That other games eventually addressed this later on doesn't really disprove that it was an issue, but rather highlights the fact that it was, or other games using the 3e engine wouldn't have had to do it differently. And all of those games involved a significant rework of the core 3e rule set, which highlights what we said about how much you'd have to change to make 3e work.
This is also a D&D specific issue AFAIK, because no other game that I recall uses three different skills to handle spotting things through sensory perception, which is a carryover from earlier editions, where Find Traps and Listen were separate Thief abilities, like noticing a tripwire was some type of specialized tasks that required special training. The 5e distinction between Perception and Investigation is silly and confusing too. Sifting through junk to find something not immediately apparent to the naked eye is not some sort of specialized skill that requires separate training. The deductive reasoning aspect of the skill might be easier to justify as a separate skill, but that's something I'd usually prefer to leave to the players to figure out on their own rather than have a skill check do the thinking for them, and would handle as an actual Deduction/Reason skill if I wanted to include it.
But if a task involves finding stuff, I'd rather handle that under a single skill—not just for simplicity's sake, but also because in my experience it is. You don't need extra training to notice that the seams that you found on an otherwise bare wall are actually a secret door. That's just a needless complication that adds extra steps. The one exception to this would be what I would term "knowledge-based perception", such as Tracking attempts, or Survival checks to find food and water, since those types of tasks require specific knowledge to attempt.
Sensory perception might work (at a penalty) to find a specific type of plant if you know what you're looking for, for example, but generally speaking, identifying a specific plant (or whatever) would require a relevant knowledge skill, such as Herbalism. So I do think that knowledge-based perception is a separate skill using the appropriate knowledge skill. Intuitive or instinctual perception (Sense Motive in 3e, Insight in 5e) is also its own skill as well. But sensory perception without specific knowledge is just "Perception" (or Notice, Observation, whatever).
Regarding True 20's skill list, it's not bad compared to D&D 3e or even many skill-based systems (which tend to have ridiculously inflated lists). But I'd probably fold Climb, Jump, etc, into a single Athletics skill (at least for a 3e based game), and Drive and Pilot into a universal Piloting skill. 3-4 skills to handle athletic type stuff is too much for a game with limited skill points that expects you to invest a ton of points into every skill individually, and vehicle operation rarely even comes up in actual play to treat every vehicle type as a separate skill.
I also don't think that vehicle operation is such a specialized task that every vehicle type needs to be handled separately, even to the degree that certain vehicles need specific training to familiarize yourself with them, cuz ultimately the core talent that determines your level or how good you are at steering vehicles is basically the same. It's more like you need to become qualified to handle a vehicle without penalty, but once you do, it's all the same thing. Granted, 3e and most systems don't handle skill level and specific qualifications as separate, but that's closer to how I view piloting vs specific vehicle types, than every single vehicle being this thing you have to level independently. Same with weapon skills. All melee weapons share the same body mechanics in my experience, you just need to familiarize yourself with specific weapons or specialize in them.
TL;DR: Sensory perception shouldn't require separate skills, unless it involves specific knowledge, in which case the appropriate knowledge skill trump Perception skill. The only other type of "perception" skill is Intuition (Sense Motive/Insight). And general skills, plus specialties and qualifications make more sense than every tiny skill variant being this separate thing you need to level independently.