Flickering at brush seams

I am in the process of building of large underground facility for my school work, and long story short, I get little white dots that flicker around some of my seams. I snapped every wall to a grid and lined them all up right against each other, but at seams in the brushes (where they were split into multiple brushes to subtract a section out for a room). Its sort of difficult to explain, but as I run around, white dots flicker around the seams. If I stop moving where some dots flicker, I can actually see the white dots just sitting there. Is there some trick to getting these dots to stop flickering and what not? Like overlapping the walls by .1 or something? The problem is also not TGE dependant, it happens in the Constructor as well as in-game.