If you want to go this route (placing vias all over the board), I'd recommend to place them in a raster (maybe 5mm ... 10mm). IMO this isn't necessary for this kind of circuit, but won't harm anyway. Another good thing to look where to place the vias: If a plane (no matter which side of the board) is slotted by one or more traces, place vias left and right of these traces, to the plane on the other side will connect over the slot.
From my experience, this board looks good enough, though it may be a good excercise to go all the way. I'm more concerned about the other board, you should do the same style redesign there.
Anyway (another IMO), I wouldn't have redone the board, but in the first place just bodged some solid ground connections across the existing boards (most important would be to solidly ground and tie together the USB and RJ45 shields) to see if this strategy helps (has done quite often).