Holy moly... Did a hedgehog sleep on your PCB, or where are all those vias coming from?
Note that specifically with regard to your board, the via stitching has no negative side effect but it also has no purpose either. Your board is neither dealing with (somewhat) higher currents, nor is it dealing with high(er) signal speeds/frequencies. It's just a simple 328P board. So, why the obsession with all those vias?
There are only two things on your board that could possibly (i am stretching the meaning of "possibly" here) benefit from via stitching (if at all).
One would be a seam of vias around your board edges which would counter possible EMI radiated from your board. The other would be the copper pour functioning as a heat sink for your VREG (using vias as "thermal vias" to connect the heat sink copper pour on the top with a copper pour on the bottom, thus increasing the thermal capacity of the heat sink). Side note: I do not expect EMI or the size of the current heat-sink copper pour to be really a problem for your board design...
With regard to when and why via stitching is recommended/necessary, read the following thread:
via stitching in PCB's (random pick, there are probably more threads here which say something similar along those lines).
Remember that i said that the via stitching on your board has no negative side effect. So, if you like 'em, keep 'em. Don't worry. Just try to understand what the reasons requiring via stitching are and whether they apply to your board...