Oh I remember now where I’ve seen those always pixel thin (independent from distance) artifacts: they showed up when I used frac() to tile a sub image in an atlas. The pixel garbage happens because the UVs suddenly change (from 0.99999 to 0) thanks to the frac(). That trips the texture filtering: the GPU tries to blend together two not neighbouring texels and thus squeezes in everything between them in the original texture.
Anyway, lose the frac() and see if it helps. Also, it is not recommended to use BSP for anything rendered so go with either decals or static mesh quads.