PCB design - Ground fill on every layer?
I wouldn't. 

If your ground plane does not have breaks in it the extra fill wont really get you anything other than adding the potential to add in ground loops and noisy mechanical edges you really do not want. Other wise I really do not see how it will "shorten" your return paths.

However, there is some merit to add fill if the components on your board are expected to run hot. Whether that fill should be connected to ground or not is up for debate. I would single point connect it to ground just so it can't build up a charge.