To narrow down your bug remember that you can turn paging off completely by constucting a fixed size volume. You can also disable compression in case this is related to the issue.
Also, you might want to implement some kind of 'reset' function which regenerates all the PolyVox meshes in you environment without worrying about whether they have been modified. Bind this to a key and run it when you see a problem. Then you can see whether it is the mesh or the volume data which has the problem.
As for your LOD question, I imagine that however you do the LOD it could potentially cause problems with triplanar texturing. You will have to do some research here or just try to minimise the problem. And as for implementing it in real time, I personally would investigate storing a lower resolution version of the volume and then generating a lower resolution mesh from that. As has been mentioned in the past, there may be cracks between LOD levels but I would try to cover them up by overlapping the LOD levels. This is completely untested though
