Unfortunatly you are right about the shadows, they are not an easy fix. They won't ever be fixed really, they are like they are because there's just not enough memory in consoles to hold a higher resolution shadow map.
If you drive the nurburgring you should notice the shadows being worse, which is because the resolution hasnto be spread over a much larger area.
You'll see the same ugly shadows in many games using the same technique, don't expect it to get any better this generation
I do feel it brakes that illusion of beautiful cars far too often, but I know they'll have struggled with it for months.
do we need shadows though - why not the option just to turn them off completely ?
like you can on PCs etc - that can't be hard to code