Finally got a chance to play my copy of RRRR DX today.
First impressions:
Really loving the drawings and animations on the menu, especially the Senile Team chicken logo. The free stickers are particularly cool (see pic)

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The music is really good, if you had a Commodore Amiga in the 90's you'll know what to expect. The DX version comes with the soundtrack on a separate cd which I'm listening to at the moment (I've not got far enough yet to hear all the tracks in game!).
As for the game itself, I'm really enjoying it so far. It's a little tricky at first as its very difficult to complete a track on your first play, but once you've done a few laps round and know the course, it really comes into its own. The car control is quite simple, but allows you a great deal of control over your car by tapping break at the right time or sliding round the corner just a bit earlier. If you go off track slightly your car doesn't explode like in Micro Machines and this allows you to try some fun detours that can shave some time off your laps in a similar way to cutting the corners in Mario Circuit 1 in SMK. Of course you can't just forget the track completely as there are strategically placed pieces of scenery that will block you from straying too far.
There are lots of nice touches during the game, such as the humans, cows etc that you can smash through on the course, complete with comedy sound effects and the way the music goes muffled when you go through a tunnel.
On my first attempt, I managed to get to track 5 (on easy) before running out of credits, but only by the skin of my teeth. After inputting my code in the online high score I found I was a poor 170th!
I've not had a chance to play the multiplayer yet (I need to find more Dreamcast control pads) so I can't comment on that.
The one issue I do have is not to do with the game itself, but the case / packaging it came in. The case uses those little teeth that hold the cd in place (rather than a more solid cd holdy thing) and upon opening my new copy, both sets of teeth had completely disintegrated, leaving the cd's loose to get scratched up. The box itself isn't very sturdy and had a few cracks in. Not that this is a problem itself (and obviously not the fault of the developers) but a bit of a pain after getting the DX version with all the cool stuff.
Anyway, great work on the game guys, and if anyone is still sitting on the fence on whether to buy it, go ahead and get it you fools.