Ah, me and the M14...here's what I'd change.
1. Front sight. The sight itself is fine; it's the sight block that's all jacked up. It should wrap around the barrel and be keyed, pinned, or soldered or such in place. Those nice sturdy ears protecting the sight become completely ineffective if a moderate bump on one dislodges the entire sight block. (And generally strips or trashes the screw in the process.)
This is by far my largest gripe. It's the problem I spent the most time correcting and is in my mind a critical design flaw.
2. Rear sight. It's fragile, so fragile in fact that if it's not bottomed all the way it can be damaged while cleaning the rifle. (Because the rifle must be held upside-down to clean in order to keep assorted garbage out of the gas system -- more on this later.) The markings are too small and difficult to read. The whole screw-through-the-middle thing was never a good idea and should be replaced by a different system.
3. Gas system. It's in the wrong place, for one thing; placing it above the barrel instead of below would place the bore more in line with the shoulder and dramatically reduce muzzle rise. It would also make turning the rifle upside-down for cleaning unnecessary.
4. The action. Locking the bolt to the receiver like this isn't a good idea. It complicates manufacture, hinders accuracy, and generally causes problems with no actual advantage. I'll say for the record that in this particular case it works and works well, but that's a testament to the quality of manufacture, not the soundness of the design itself.
5. The bedding system. It makes dismounting and swapping stocks a snap and sucks in all other regards for numerous reasons.
6. The safety. It works and it's pretty quiet but it's extremely difficult to operate with heavy gloves or mittens. It would be nice if it could be engaged without charging the rifle first.
7. The handguard. They break easily and they're a hindrance to accuracy as implemented.
8. The flash hider. They are far too constrictive and all should be reamed out to NM specs at the very least. If they're even slightly misaligned (and they do occasionally show up from the depot like this) you'll know it from a crazy zero and gilding metal streaks on the interior. If it's more misaligned than that (I've seen a few) the flash hider gets shredded.
9. As Noah said, the ROF is far too high. It was an abject failure as a FA weapon, although I'm not sure that a lower ROF would completely solve the problem. The thing's just too light for that, and without a straightline stock...
10. It would be nice if the buttstocks accesories actually fit in their assigned places from the start...at least, without the use of a rasp. It would also be nice if pliars weren't occasionally required to get them back out. The end user or armorer can fix this easily enough but shouldn't it have been fixed before it left the factory?
11. The charging handle is on the wrong side of the rifle for right-handed users.
12. I've never liked rock-in magazines. Even with practice it's easier to screw things up than it is with magazines that go in straight.
14. From a manufacturing standpoint it's a nightmare. That doesn't affect me or you but it does affect why we can't purchase rifles built to military specifications -- because nobody can make them, at least not for a price that most could afford.
To be fair to the rifle, it's based heavily on a design that predates WWII and would have to be basically a pre-war rifle without massive design changes. Semiautomatic rifles were a fairly new thing at the time and we didn't know then what we do now. This does not excuse its flaws though; the US had several opportunities to pursue more advanced designs with far fewer intrisic defects and chose not to, and if it's going to be brought up as a good choice today (which people tend to do) it must be compared with the other things that are available, even if they're newer designs.
