In no particular rank/order:
1. Proper use of signals
2. How to park
3. How to merge
4. Which lane to use on a # lane internstate and safe travel speed
5. Keep windows clean for optimal visibility (that layer of film/dirt on the outside AND inside of your window can get dangerous when the sun is at a certain angle or at night with oncoming traffic)
6. Tires. Proper inflation and how to change a spare. Recognition of tires that need replacement.
7. Traffic signs
8. Windsheild wiper blade replacement so you can actually see out the car when it rains
9. Proper mirror AND seat adjustment
10. When to recognize that your car needs to be fixed and not driven till it won't even run
11. Everything else I forgot that contributes to safety
I wouldn't say people need to know how to work on a car (other than the few things above). That's what mechanics/dealerships are for. I honestly don't care if someone does or doesn't know how to change their own oil or brakes or rotate their tires, as long as they get it done. At the very least, people just need to learn how to drive and properly maintain their car for optimal safety (like example 5).