Clicking randomly in the blank scene window does cause game objects to be selected in the Hierarchy Window, and the Game Window is rendering fine (and the game runs). But the Scene Window is simply blank for several (not all) scenes in the project.
The Scene Window does however render the scene when the “wireframe” rather than “shaded” shading mode is used.
There is a message in the console that reads:
Can't add 'UniversalAdditionalCameraData' to SceneCamera because a 'UniversalAdditionalCameraData' is already added to the game object!