The drivers side hood does not go all the way down on back side of hood where the hinge is mounted. Just started doing this. After you close the hood, the back is stuck up about an inch and you can push it down with your hand. What's the cure?

Lubricate the hinge.

What's would be the best lube for that style hinge?

Be cautious when closing the hood just in case the hinge is shot. Don't want it to bind and bend the hood with lots of pressure. I've heard regular motor oil, to silicone spray, to WD-40. I have some Endura Penetrating Grease I am going to use on mine. Someone on here recommended it for door hinges, so I got a can from Amazon.

Hood hinge bolts loose or hood hinge area rusty? They tend to rust in the hinge area from the inside out and weakens the clamping force. Then the hood slides around. Witnesss marks on hood?

On My A-body it did that until I adjusted the hinge better. If nothing is rusted or bent you may need to adjust how the hinge is connected.

I think (if I remember)that you move the rear of the hinge up on the hood.

Anyway, I sounds like an adjustment to me. I does need it's lubrication as well.