Why do my wheels do this?

Hey guys,

I am trying to get a car up and running in Unity 5. I am trying to use a car I found on the Asset Store with the Car Controller script from the Standard Assets. It works.... The car can drive forwards/backwards but the wheels are all messed up.

To begin with, in the Scene view the wheels are where they should be and everything looks good, but as soon as I hit the Play button, the wheels will "jump" off the car and offset themselves away from the car. Below are pictures of Scene view and what happens in Play mode:

Imgur album with scene/play images

I tried adding layers to the wheels and the rest of the car and disabling physics between the layers since I thought the wheels might collide with the body and be forced away but that didn't help.

Also, when the car drives, the wheels are spinning around really fast and one front wheel can be rotating clockwise while the other is anticlockwise and it looks really weird.

What could be wrong?