1975 280z
Two issues.
1. The engine idles at 1500 rpm and I can't figure out how to get it to slow down. I am aware of adjusting the dash pot and the other screw thru the long spring. There has to be something else that is causing the high idle problem. And then, all of a sudden the engine will idle as it should for a moment and then back to high idle.

2. Also, the engine cuts out spuratically, with no sputtering or warning. The starter will turn the engine over but the engine will not run. All indications show there is proper circuit voltage etc. Then after awhile, the engine will start as if nothing is wrong.

Can anyone give me some advice as to where to start looking for these problems?

I would suggest just cleaning all your sensor connections. If you see a greenish color, or the contacts aren't shiny. Get a toothbrush and can of WD-40. Gently spray the area on the contacts, and clean with the brush. Let air dry for a few minutes. Then hook them back up. The fuel injection system can be finicky when things are not working right. That should give you a start. I am also sure there are less sensors on your Z compared to my 280zx. Anyway, there are other things to check. But try those first. And good luck.

Oh, and welcome to Zdriver man.

The likely cause is the BCDD valve, It is located on the bottom side of the throttle body. It's purpose is to allow more air when the throttle is closed under deceleration. Don't know what part is causing it maybe the valve itself. To solve the fast idle just plug the hole inside the throttle body located just in front of the butterfly. It won't affect performance except it will run rich on decelleration.
Your fuel pump is failing intermitently. Soon it won't come back on at all.