So I've been running through the demo for the past couple days, and I've decided to share my thoughts about it. (Note: I'm not an expert reviwere, and all of this is in my opinion.)
First off,
Graphics: The Graphics in The Run, while not the best, is still definetily superb. The lighting is ver good in the Desert Hills run, but seemed to be a bit on the bright side when driving Independence Pass. Speaking of which, this level also gets a good chance to show the Frostbite 2 engine. The explosives flying into and detonating on the mouintains do divert your attention for a bit, as does the snow falling off. Independence, to me was the best looking level. The damage model though, especially after you wrecked, was pretty lackluster.
Physics: The physics in The Run are very good, especially since brakes actually help out now.

It doesn't have many sim elements a la GT5 or FM4, so don't expect anything special in that regard. There seems to be some differences in car handling, though. The 911 Carrera S seemed to be very agile and goes through the corners nicely, While the Gallardo LP-550 would try to mess around if you went through a turn with to much enthusiasim. When driving through I.P., though, the cars will definelty need a bit more finesse to keep on the road (and keep up), as the snow creates some understeer. Driving on the bits of blue ice will result in mad understeer, so it's probably best to avoid those. Overall, these are some good "arcade" physics.
AI: Now, as stated earlier on, the ability of the AI does change depending on the difficulty level. So, when I tried on hard, I found that the AI was pretty fast, although once I got the hang of the game, I was easily able to push through the opponents quickly and stay up front. So, I decided to try Extreme. On this setting, if you give it a go, the AI will really give you a fight. They will have no problem keeping up in speed. If you come up close to the side of another driver, they'll probably try to sideswipe you off the road, which can make for some terrifying moments if you're not careful. They also will overtake you if they get a chance, so it's not like once you pass you don't have to worry. The other guys will be on your tail. Also, there is a catch-up mechanisim, but it's not as pronounced in previous games, such as Hot Pursuit. I found on Extreme, it'll only kick in if the guy is literally right in front of you. So Overall, if you go for higher setting, don't expect an easy win.
Sound: Simply

. Every car sounds awesome! You can definetly tell when some one is right behind you and wants to pass. The sounds are especially good when you're being passed by. The V8 from the Camaro ZL1 as it overtakes you is a simply loud, in-your-face kind of sound. You can also clearly hear the sounds of the rocks and snow falling on the road in Independence Pass, which adds greatly to atmosphere as you try to survinve the race.
Overall: The Run Demo is simply great. It does absolutely nothing wrong in terms of the overall package. However, if I'm honest, it does many things right, but nothing very noteworthy for me, other than the sound. This is something like Dirt 2, a very fun, well made game that provides a good bit of entertainment. I do think, though, that the full game will be an awesome thing.
Grade: B+