I tested in chrome and FF and i can't see the white gaps across the top
I can see them slightly in the editor though, but 'view grid' was enabled and the grid has light and dark pixels.
a few other things though..
If you put one of the wall blocks on their own a bit lower, and zoom very close.. you can see that it is not totally flush with the black lines of the tiled background along the top and left edges
you should make the tiled backgrounds hotspot top left.. it works okay at sizes that are multiples of the grid*2, like the size of the window, but if it was any other size you would have alignment problems.
also setting the sampling mode to point means you can do things like have solid colour 2x2 sprite and stretch it to any size whilst retaining the hard pixel edges