So how does this game compare to other games in the series, particularly MKDS?
Personally I think this is the best Mario Kart in the series. In terms of polish and presentation there isn't much to argue about --- the game looks fantastic, runs at a buttery smooth 60 fps, and has tons of interesting visual variety in the tracks, character models, and karts. The 3D effect is also surprisingly nice, I haven't turned it off at all during my time with the game.
The new tracks are almost all fantastic. Even the tracks that I didn't like at first have grown on me for the most part, and the consistency from one to the next is particularly impressive. There is a great deal of variety but the core gameplay is solid regardless of the track. In general the width of the tracks has been reduced in comparision to the Wii tracks (thankfully) and there are a good number of short-cuts and alternate routes strewn throughout the layouts. The retro tracks are also very well done, especially the SNES and GBA ones. My only complaint regarding the tracks is the DS selection --- I think they could have done better. Still, all the retro tracks that were selected are quality.
Vehicle customization is fairly simple but remains interesting thanks to the multitude of potentially viable options. I haven't really noticed many trends in my online races regarding a specific kart, character, or set of tires, which is exactly how it should be.
In terms of gameplay I find MK7 to be one of the best in the series with regards to skill/luck ratio. There are still numerous victories that occur based on "right place at the right time" item selection (particularly with blue shells) but that isn't really anything new for the series. In my experience the best racers will still usually rise to the top, and "fluke" victories are not a very common occurrence. The item chaos has been toned down since MK Wii (this is also helped by the reduction in player count from 12 to 8) and there aren't really any items that feel completely unbalanced. The addition of coins is also a huge plus as this adds another interesting skill-based element to the races.
Drifting doesn't require as much skill as it did in MK DS but I find it to be much more enjoyable. The drifting model is essentially taken straight from the Wii version, so snaking is all but nerfed out of existence and the two boosts (blue and red) that you get from drifting are based solely on how long you drift and how hard you turn into the drift. Harder drifts get you the boosts faster, in other words.
The game modes are fairly bare bones but I don't imagine most people will mind that. The only mode I really think the game is missing is a single race option --- as of right now your only choice for playing a particular track is going through it in a cup.
Online is much better than I expected but still has room for improvement. Communities are typically great fun (as is evidenced by half the posts in this thread) but the lack of control within them is somewhat disappointing. Sometimes it's hard to find a game with enough players and there are no other standard race options besides a full four race GP. Still, the netcode is solid and the game is a blast to play online, either in the community or against random players (for when GAF is beating you too badly).
So yeah, in summary I think this game is a solid win for Nintendo and the 3DS. I don't see myself dropping this one from my rotation any time soon.