Can't really speak for 0e, so I'll start at 1:
1e: Too much complexity where it wasn't needed (weapons vs. armour type, weapon speed, etc.), some odd and oft-ignored ideas such as ExP for g.p., arbitrary racial level and class limits used to balance out racial powers, psionics were a mess, bard was a mess, two-classing was a mess, not enough thought given to how spell A might interact with spell B thus lots of need for DM rulings, much of Unearthed Arcana was just broken, lots more minor niggles.
2e: Too obviously an attempt to appease the religious nutballers, also too obviously an attempt to market the game to a younger audience, THAC0 was never necessary, wizardry schools were a mess, later too much repeating bloat, but overall just so bland as to be very forgettable.
3e: Too. Many. Rules. Emphasis shifted from character roleplay to character build, wizard schools emphasized even further, rangers started as pathetic then were errataed and 3.5'ed into pure wackoland, dungeonpunk look and atmosphere, illusions nerfed, too many buffs and other ways to change or increase base stats, hard to kitbash, level advancement too fast, ExP calculation a nightmare if party includes a range of levels, multiclassing was a mess, too many spell nerfs in 3.5 along with poor solutions to unnecessary problems (polymorph, I'm looking at you), sense of mystery lessened as players gain more mechanics info e.g. base attack bonus, and many more. Oh, and bloat bloat bloat.
4e: Balance overkill, reality simulator switched off completely, too focused on the grid (thus, square circles and cubic spheres), advancement sped up from already too fast, bizarre race and class choices at startup, sense of mystery further lost as magic item write-ups now in PH, jury still out on many other things.
Odd, that when I look at what I've just typed it seems obvious I have the fewest problems with 2e, yet of the 4 it's also the system I'd least like to play or DM.
Lanefan