Ideally, this device would be a flat screen type object that you could put in between your eyes and a real, live, circuit board, which would display the actual voltages/currents over top of the actual traces and components.
How would it actually work? Hmm... That's the part that isn't baked yet.
:-)
First, electric fields could be sensed with a dense array of electrometers.
See the array of electrometers in the link. This idea could obviously be made a LOT smaller. (the screen I am typing this on has a few hundred transistors and LCD elements per inch.)
Is there some way this could be focused to make an image of the board, though? I imagine you would have to hold the electroscope array right next to the circuit to get a sharp image. Is there a "lens" for electric fields to form a sharp image?
Currents could of course be detected by the magnetic fields they generate, but I'm not sure how you could form an image like the electroscope array.
And, of course, AC would not be clearly visible above a few hertz. You'd have to have some kind of visualization for DC voltage/current direction and AC amplitude/frequency. Seems possible, though.
It would make troubleshooting and designing things a LOT easier.