The Vista Cruiser has no rear-view mirror.
The gym would definitely not be a bomb or tornado shelter. A large open space under a large roof is the last place you want to be in either situation.
When the tornado is in the road, following Eric in the car, another car is not just seen, but accelerating, *toward* it.
Eric had no idea a tornado was behind his car. During a tornado, there would be strong winds and debris, but the air was calm. He would have noticed some kind of weather change, like humidity, rain, wind, etc. The tornado comes and goes without leaving any signs of blowing through.