There were quite a few that looked nice, or at least decent, back then. Now it seems like people focus on making it look as cheap and quickly as possible with a complete lack of detail or regard for anatomy. I just dislike how a lot of shows follow the 'noodle limb, big head' approach, like
Flapjack,
Adventure Time, or Fairly Odd Parents (though Butch Hartman uses a more angular style than noodle style. Shows like Total Drama Island and Johnny Test also apply to this) If we go into the 'attractiveness' area, then I'm also not sure how anyone could find those characters attractive (I know there's people who do, believe me, but I'm just saying.)
Judging by those shots, they look better than Samurai Jack's (which I found too bland and simple), but they don't look too terribly impressive either, there's a lot of flaws in them (like certain objects not being colored, or colored outside the lines, or lacking those defining lines to begin with. Not to mention it still looks flat and detailed on certain objects; like those melons in the fruit stand one, or how the apples just mesh all together with squiggly lines. And maybe it's just an aesthetic preference, but I dislike how the lines look grainy and unfinished, rather than crisp and polished) Though production art looks different than from when it's in the actual show (sadly, it looks worse in the show usually) so we'll see how it is in the actual show with the characters in them as well.
One reoccurring gripe I see is lighting (not just with those, but a lot of series); it seems to be a hard thing to do for a lot of people. Lighting seems to come off very flat and not as vibrant as it should. Scenes like
this and
this show of some decent radiance, or
this for a sunset. Again, using the fruit stand one as a comparison, that lighting seems more flat and artificial, despite a clear line where we should see the light. (And those are just random caps I have from a random episode I picked; I'm sure I could find better if I actually looked for good scenes, but they also show off some decent background work as well so I picked them)
My cousin who's 11 can draw Adventure Time exactly on-model; and he's really not that good of an artist; so I'm going to place that to the fact the designs are so simple. Looking at Flapjack and similar shows, it seems there's rarely an 'on model' considering how much they squish and stretch their bodies at random time, so I'm not sure what you mean by messing up.
Takahiro Kagami is a really nice director; I saw a tribute video to him one time and really adored it. A personal favorite artist/designer of mine is Kenetsu Satou, who draws awesome characters and background designs, which translate very beautifully into animation.