I don't think your sentences are a proper exemplification of the type of error you are talking about here.

In your example, "One of the cars is red" is always correct. Never use "are" in this situation.

The more common error arises from a different type of grammatical construct involving clauses.

These sentences work:

1. One of the cars is red, and is parked in the driveway.
2. One of the cars that are red is parked in the driveway.

The first sentences means that one red car out of all the cars (whether they are red, blue yellow, whatever) is parked in the driveway.

The second sentence means that all the cars are red, and one is parked in the driveway.

you are the MAN.

One of the Car IS red is correct.... If you see that clearly points...only one among many car... so it is singular....