The problem with S3&K, in a word: clutter.
It’s a problem on a micro, a macro, and a lukero level. It’s a problem with nearly every design element from art direction to level design to game structure.
What good ideas are there — and there are some good ideas — are smothered by reams of noise. Sonic 3 was bad enough, both being cluttered and clearly unfinished. Put the second half on, though, and what you get isn’t a complete game. It’s a game that was complete once, then someone fucked with it for six months to make it bigger. For the sake of being bigger. More full of stuff, for the sake of having more stuff in it.
It needs an editor. Badly. A third of the ideas need to be killed. Half of the levels need to be removed. The levels need to be redesigned with some focus to them. Somewhere along the way, someone needs to ask just what the game is attempting to accomplish, both in a grand sense and at any individual moment.
And redraw the damned graphics already. Jesus. Stop pretending all the sprites are digitized clay models. Learn how to use the colors you have instead of pretending you have a larger palette than you do.
A good game could be made from Sonic 3 & Knuckles. It’s not a bad starting point. On its own merits, the thing is just a ridiculous mess.
Speaking as an editor.