In Godot latest, 098c7ba4f, on Windows 10 with GeForce GTX 970, I have significant shadow artifacts on a simple scene with multiple lights.
My scene has just a sphere, a floor, and three directional lights (Warm, Cool, and Key). If you open the attached project in the editor, you'll see big stripes on the floor even though there's nothing to cast such shadows:


Also if you turn off CoolLight and turn on the other two, there will only be one shadow: the KeyLight shadow has disappeared.

You can see various other false shadows and disappearing shadows with different combinations of lights turned on/off and moving around the scene.
Steps to reproduce:
Download the attached project
Run in the editor
Orbit around the central sphere
Observe the stripy shadows on the floor that move as you move the camera
Turn on and off various lights:
Minimal reproduction project:
shadow-test.zip
It appears that Godot only shadows for a single directional light. In fact, it almost appears that just about all the rendering assumes only a single directional light. I vote that at least up to 2 directional lights are supported, or at least two with shadows.
This seems to have been fixed in the master branch (with the new Vulkan renderer), closing.

Most helpful comment
It appears that Godot only shadows for a single directional light. In fact, it almost appears that just about all the rendering assumes only a single directional light. I vote that at least up to 2 directional lights are supported, or at least two with shadows.