Okay, I finally tried the demo out and it has definitely piqued my interest. Crashing is, of course, excellent. Watching a slow motion sequence of my car crumpling into a small cube of metal as I ram it into a concrete barrier at insanely high speeds is very satisfying (as are takedowns, and any other wrecks). The graphics are also wonderful, especially considering all of the environmental details present. They've done a nice job making Paradise City look believable. There was always something about NFS:MW, for instance, that just didn't seem quite right--at least in some areas of the game.
As everyone's already said, the mini-map intensive racing is frustrating. Some trial and error is to be expected to get a feel for the race and to know when to turn but sometimes it looks like your turn is coming up according to the map, but it's a shortcut or side road and not the path you want to take. Checkpoints would be nice--it could at least show you a general route but still allow for shortcuts.
The biggest problem with regards to this issue, though, is the fact that you can't restart the damn race! I know it's been mentioned, but I think this is completely unacceptable. It makes no sense to force you to drive all the way back to the beginning. That's just boring and discourages me from wanting to race. It also creates an even higher learning curve, since you can't just instantly restart and try again.
Some other things I noticed that I don't think have been mentioned:
--If you let your car sit for a short while, the engine will turn off. After a few more seconds it will go into letterbox mode, turn black & white, start playing classical music, and give a very low aerial fly through of the city starting from wherever your car is parked.
--There's no driver in the car. Is this a more mature "Cars" universe?

This is a good design decision, actually. A driver is just wasted polygons in a game like this.
--There's a paint shop, but it's GTA "Pay 'n' Spray" style and won't let you choose a color. I realize Burnout isn't really about customization, but if it offers you the option to change your vehicle's color, it should at least let you choose. Hopefully there's something in the full game that will allow this. Not really an issue, though.
--The camera controls suck. If I point my analog stick to the right, I want to look to the right, not look at the right side of my car. There's no option to un-invert the camera controls (that I could find, in the demo anyway), so I can't really use them. Not a huge deal, but I found it to be annoying.
--I can't help but think that this game could definitely benefit from a Theatre Mode. Just imagine the cool films you could create from elaborate crashes that you coordinate with a few buddies online. :evil:
--I thought the radio host thing got annoying after a while.
Otherwise, this game seems like fun, but if it's going to be this hard to find and participate in races, I'm not sure if I'll be able to get into it as much. It's certainly made my watch list, though.