The editor by default uses FXAA as the anti-aliasing solution. Once you enable the game-mode you get the runtime anti-aliasing solution which is a form of Temporal AA. The transition when toggling between FXAA and Temporal AA can leave some artifacts on the screen. Once the view is moved the artifacts go away.
As for the noise material case, the Temporal AA requires accurate motion vector field in order to work correctly. Quickly animating a material on a surface does not generate any motion vector field so the Temporal AA has a problem in that case.