Using QGIS 2.14.3 I tested Virtual Raster Table technology for the first time using two TIF DEMS (NED 1/3 arc-second, projected to EPSG:3338, single band, 32-bit floating point, ~ 5-meter resolution). I then created a GeoTIFF hillshade from the VRT (using Raster > Terrain Analysis > Hillshade). I think that the results are spectacular (Brooks Range, northern Alaska):
Happy with the above test, I then used the same procedures to create a VRT for my entire project area (77 NED TIFs), including a hillshade. Sadly, though, this hillshade (~ 70 GB!) has an unwanted grid pattern:
The same process is applied in both cases, the only difference (that I can think of) is the number of TIFFs in the VRT. The grid pattern reminds me of improper resampling techniques that I've seen in the past (such as using Nearest Neighbor when Bilinear would have been appropriate), but even still, why did it work so well in the test case? Any suggestions to avoid this grid pattern?
EDIT: After further experimentation, I have found that this unwanted grid pattern arises when as few as two tiles are used in a VRT.