How to make each scene keep its viewport position? The viewport camera position is global, so when I'm switching between scenes that have stuff at different locations in the 3D space, I have to continuously move/rotate the viewport so that it looks at something meaningful. 

Is there a way for each scene to retain its viewport location/rotation?
You can use local camera in each scene/viewport.
It works reasonably well.

Choose a camera and set it as Local Camera.
And then check Lock Camera to View

Set the View panel like in this gif.
Note that I use a different local camera in each scene/viewport.