Okay, since oxybe asked nicely, lets look at some of his problems...
the disparity of scope between full casters and everyone else is highly jarring. for the most part you're either a sword-swinger (or slightly glorified version thereof) or you're telling reality to sit down while the adults are talking.
magic doesn't really have a limit or any real concept beyond some superficial elements and how it's cast. stuff is often either extremely mundane or magic and magic seems to be capable of doing anything and everything with a little tinkering.
I'm going to combine these two together because they seem part and parcel of the same complaint... magic is magical...
yes...
Okay...
Alright, I confess I'm not really sure what the complaint is here. Of course magic is magical and able to accomplish non-mundane things.
Now, if the question is whether or not non-magic users can perform on-par with magic users, I would postulate (and have often in the past) that they can. In their own way, the fighter and rogue (two of my favorite classes) shine brightly. While granted that the high-fantasy tropes expect that the rogue is going to eventually get some sort of nifty magical gear that allows them to shadow-walk, and the fighter is going to get Exbladius Magnificus, the sword above all other swords, these classes rely on not using spells to accomplish their goals and the satisfaction in playing them should come from their cleverness and strength. If the wizards are outshining these classes, I would suspect there is a DM problem somewhere that needs addressed. (and if this is the case, and if you are willing to be open-minded, then we can address some of the things that might be causing this)
Now, if the complaint is that you want a world in which there is not a lot of magic, then you need to make some serious changes to the class options you give to your players, change the setting, and learn how to run a grittier style game (which can be done).
classes on a conceptual level. some, like the wizard, are supposed to encompass a wide variety of character archetypes while others, like the barbarian and monk, are pretty obvious in what they're going for.
Again... yeah... I'm not sure I see the problem. The monk and the barbarian encompass less stereotypes (they are in fact stereotypes in and of themselves) than the more generic classes. Why does this bother you? The classes are tools which you use to build the character you want and if a certain class does not work for what you want, use another one. If a certain class works for someone else, more power to them. They are just options and, generally speaking, more options doesn't seem a bad thing to me.
feats are a mess, conceptually and in practice. they cover a wide array of things from simple skill ups, making certain assumed normal techniques useable or opening entire new uses of existing resources.
As with classes, use the ones that appeal to the need you have at the moment. Ignore the others. If you have feats that work for you, then those are the ones you need at the moment. Why should every feat be exactly on par with every other feat when their purpose is to serve as a set of options with which to focus and customize characters? The feat that focuses on skills is useful if you are a skill monkey and a feat that focuses on combat is useful to optimizing fighters. This seems more of a feature than a bug.
Now if you have a complaint about a specific feat, that might be more useful. But understanding the purpose of feats, it makes sense that they would cover a wide variety of options.
skills are too granular and most characters don't get enough points to be seen as skillful. it also takes a while before you get your skills up high enough to be successful with a good consistency.
This is not a problem in my games. But, if you are finding your characters to be skill deficient there are some things you can do to alleviate this. Firstly, don't use intelligence as a dump stat. Never play a character with a lower than 14 intelligence if you want more skills. (You can also consider playing more humans of course). Also talk with your DM about exchanging a class feature for 2 more skill points per level at character creation. Generally speaking, you can get rid of any one feat like class feature for 2 skill points/level. So for a fighter, for instance, you could offer to lose your heavy armor proficiency, or with a wizard, drop Scribe Scroll.
As for skills getting high faster, there's a feat for that. I must admit that if I have a character I want to be good at something, even at 1st level, its generally not a problem to have a +10 bonus to that one skill right out of the gate (4 from class, 3-4 from Ability, 2-3 from Feat, and even another +1 from traits if you want).
Now, as for the complaint that not every character is skillful. Why should they be?
If every character can cast spells, and every character has the exact same feats doing the exact same things, and every character is equally good at skills, it seems to me that the variety of meaningful character choices is going to be pretty small.
weapons as a whole are pretty boring, with them basically just being a venue for dX worth of damage. the weapons are, for the most part, a slight variation of damage dice, damage type and weight in any given category.
magic items, especially weapons, don't feel magic. a slight bonus to your hit and maybe a minor damage effect doesn't really make it feel "magic" then again, i grew up with the mythological stories of Excalibur, Mjölnir & Caladbolg.
The complaint that weapons are boring is a strange one to me. A weapon is a weapon like a hammer is a hammer and a 50 foot length of rope is a 50 ft length of rope. If you want less boring weapons, there is nothing for it, but for the DM to do more work to make each weapon unique visually, story-wise, and in impact in-game. Personally, this seems like a lot of unnecessary work for me, at least to do it for every weapon; I think it should be done for some weapons.
If you want your character to have a weapon with more personality right from the beginning, take an exotic weapon.
Or, if you want characters to possess weapons with story, then the DM has to give it a story. There is no shortcut here. The weapon should be written up with a description, a certain amount of history should be given to it, and it should have a name. The name is really what makes a weapon special. A soldiers gun is just a gun until he names it. And then its a companion. The same is true of swords, knifes, etc.