> If marking chalk on a car is trespassing then wouldn't throwing a newspaper in someone's driveway also be trespassing?

Yes, without permission, dumping on someone's property is a trespass.

> So to would leaving a hand print on someone's car if you happened to touch it.

It is a trespass, yes. Probably not on its own an actionable one (or at least not one worth civil action) because of the lack of harm, but whether a trespass would be actionable or worth action as tort is irrelevant in the case where you are looking at a Fourth Amendment violation where any trespass by givernment for gathering information to be used against a person (as a violation of legal property rights) is, ipso facto, a violation of an expectation of privacy, triggering the requirements associated with a search.

Nonsense. Trespass is deliberate interference with another person's property right. Does a hand print or chalk mark prevent someone from making use of his car? The answer is obviously no.

So you can vandalize my car with chalk all you want as long as it doesn’t violate my possessory interest?

If you want your car to remain in pristine condition, keep it in your garage. Don't park it in a public space. In a shared space undesirable things happen. Just because you object to something doesn't make it a crime. Guilty mind plus guilty deed make something a crime.

Isn't vandalism different from trespass?

Vandalism is a form of trespass.