It's a great entry into the series, while not perfect the flaws don't hurt the overall fun to be had with the game.
The 3D works really, really well. Although, I usually end up moving my 3DS around while playing which then puts the 3D at an angle that it hurts my eyes. So end up turning it off to prevent that.
There's a lot of new faces to the kart racing scene, ones that I have personally been waiting to use for many years. Such as Lakitu and Shy Guy. Shy Guy was in the download play version of Mario Kart DS, but he's never been a character on the full roster before. The obvious veterans like Mario, Luigi, Peach, Toad, Yoshi and Bowser all return.
The coins make a triumphant return from Super Mario Kart (SNES) and Mario Kart: Super Circuit (GBA). They're purpose is much different, and much better in my opinion. You can collect up to 10 coins per track (40 per circuit). They're scattered across the track, each new lap 'restocks' the coins so you can pick them up again. In Time Trails, the coins don't restock each lap. They also offer a slight boost in speed when you pick them up, making it worth picking them up even when you have 10. You lose 3 coins each time you're hit by an item (shell, banana, etc) or hazard (fire, crabs, etc).
The coins also unlock parts for you kart. New gliders, tires and bodies. Each with their own stats allowing for customization. Which is a great addition to the Mario Kart series. There's a set amount needed to unlock each new part.
The two new ways of racing are great. Gliding and Underwater. Gliding is pretty neat, it allows you to drop from gliding whenever you want so you can choose to try and keep gliding for as long as possible or drop quickly. Some levels have air flows that will keep you afloat longer as well.
Underwater gameplay is pretty much the same as regular driving, it's just a little slower and your jumps fall slower too. Sadly, the Bloopers' ink doesn't wash away when you go in water. I think that it would make sense for it to, given that going on a dash pad will wipe it off.
The new item Lucky 7 (or whatever it's called) is meh, it gives you 7 items circling around you. Letting you use them all, but people can run into the items and steal them. (like the star) So you can risk keeping it until you need to use each item (I believe that which item you use is determined by what item is closest to a certain point, what point that is I'm unsure of).
The blue shell is sadly too common, it's the one downside to the game in my opinion. From my experience it's at least 2 blue shells per level. It can hit anything on it's path like the blue shell from Mario Kart 64, but also flies and explodes like the shell in Mario Kart Wii. It has no wings though, and since it's flying it swoops down to hit anything in it's flight path to #1.
There are 8 cups in total. 4 cups with all new tracks. 4 with 'classic' tracks. The new tracks are great, and really use the new ways to race well. There are a few tracks that don't have laps, but instead have 'sections'. It's a straight run through from point a to point b. Those are some of my favorite tracks. The classic are from each game including DS and Wii, despite them being recent releases.
There are Single Player, Local Multiplayer and Online Multiplayer options. As well as the Mario Kart Channel, which using SpotPass downloads ghost data to race and allows you to join 'communities'. I haven't done much with the community stuff so don't know much about it. The Single Player offers you Grand Prix, Time Trails, Balloon Battle and Coin Runners. I would assume Local allows you the same as Online which allows you to race and battle. I can't check for myself.
The online works great overall, but getting with a friend is more difficult than it should be. You have to add their 3DS friend code. Which is fine, and works much better than the per-game FC the DS games used. The problem is that one of you has to already be playing for you to be able to join them. So if you're planning together while talking to them via chatting or on the phone, then one of you will have to join a random game. While the other one will have to keep trying to get in. Usually you get put into a full game, so that's why it's harder than it needs to be. My friend had to wait until I was through with a race to actually join, even though we started playing for the sole purpose to play together.
I've only been disconnected once (all the players I was with were from Japan, not sure if that's why). I haven't had any issues since, no lag either. It works just as well as Mario Kart Wii's online does.
After you get a gold trophy in every cup of 150CC, you unlock Mirror Mode as veterans to the series are most likely used to. For those unfamiliar it allows you to race each track mirrored. So left turns are now right turns and vise versa. Everything is reversed.
It's a great game, it has a great online, some great new features, new characters, great new tracks, great classic tracks, customization and is one of the best Mario Karts in the series.