Does anyone know how to correct this issue? When I push a polygon into the mesh to remove it, the adjoining polygons don’t go with it. During the move the action seems to be working but just as the polygon face snaps into position with the far face, the adjoining faces appear. The picture below shows the poly in motion, just before it snaps. The image on the right is the resulting mesh with shell faces.
Try using thte qmesh option on the poly, that works for me.
right-click on a polygon and switch align to “full step” 
Reduce the size of your brush falloff (draw size). It will be more precise.
I get the same problem when my brush size is too big for the polygons Im working with.
I’ve moved this to the Other Questions and Troubleshooting Forum which is the best place for this sort of thread.
Thanks everyone for the help. I’ll try those suggestions tonight. Currently too busy working on taxes, ugh.