The lighting's basically down to Edward Brown retiring as DoP and being replaced by Marvin Rush, is it not? I think it gets more noticeable as the series goes on, so possibly Berman's preference for all the bland things in life has a greater impact. Rush was perfectly capable of dark, moody lighting - DS9's Crossover, for example. Brown seemed to use more gels and coloured lights, which were starting to look dated by the late eighties anyway. His setups were pretty unforgiving on the sets too.
Also there's a new title sequence, new uniforms, new phaser props, all of which looked more expensive and modern, plus a new Enterprise model which allowed for more elaborate visual effects on a regular basis.
I might be completely wrong on this, but didn't they move from 2" tape to 1" in the third season? Though if that were the case, you'd expect the first two seasons to look better. Probably rubbish that I've half-remembered from another show.