Most places have a "burnout patch" so you can spin the tires before hitting the track. Otherwise, it leaves burnouts on the carpet. This doesn't hurt anything, but some people find it unattractive.
1/12 and other pan car racers will scrub their foam tires in the groove, and that is ok. It's part of getting the car ready to run.
Paragon smells like wintergreen or bengay. This bothers some people. Some tracks allow only "odor free" like Jack the gripper or SXT, Sticky fingers, etc. These are just as bad or worse for you, but they don't leave a lingering aroma.
As far as tires,any on road tire foam or rubber will be fine. You need to worry more about minimum ride height, rubbing bodies, and protruding screws or other objects.