Random nitpicks:
1) Hm... Something's off at 0:14. Not sure what. It's not sounding that "big", and it's kind of cluttered, but only because of the levels, not the number of instruments (because something like this is doable). At 0:16 though, it'd be pretty funny if you put a brass hit.
2) 0:18 - snare is very quiet, kick is buried
3) 0:40 and other similar spots - cymbal is buried
4) 0:50 - the chiptune lead sounds oddly upfront and loud, especially after the quieter previous section.
5) 1:07 - piano sounds a bit mechanical in its timing and velocities.
6) 1:51, 2:11 - sounds pretty piercing, especially on that high note. Dunno why the piano is doubling up with some sort of high synth lead in unison. Maybe the synth lead there could be sent backwards with some reverb and slightly lowering the dry mix? Additionally you may want to fade it out with some automation and then bring the volume back up later, maybe.
7) 1:56 sounds like a chance for you to create a cool chord progression and give a sense of a new section coming up. This is essentially chiptune jazz, so I'd expect jazzy harmonies.
2:16 - piano here sounds especially upfront and exposed, and it sounds a bit dry and a little bit mechanical. Sounds like what Byproduct may be hearing.
In general I'd consider points 5 and 8 the most beneficial to work towards fixing, followed by 1-4, then 7, then 6.
0:50 sounds okay to me in terms of arrangement, though a connecting sound may help tie it together with the previous section. It does go from a pretty full section to a very sparse section. Overall, this is pretty cool, man. Tighten up the production some more, and let's polish this up!