Polygon Splitting = Float Imprecision ?

Hi I have been working on a leafy BSP. It''s all working very well except that when I run through the level I can see very tiny holes where the back-ground color is showing. They are very small and when you walk through the level different ones pop up. Sort of like an old grainy film. The holes seem to pop around distinctive lines which I assume to be where the polygons are splitted in the BSP. The only conclusion I can come up with is that this is some sort of float precision issue. I don''t see why though, since the polygon splitting function assigns the exact same coordinates along the splitting plane to the right and left polygons. I checked them manually by outputting the splitted polygons'' coordinates to the console, and the shared edges have identical vertex positions. So I really don''t see why I''m getting tiny gaps in the level. Has anyone ran into a similar problem or can guess why this is happening and how I could possibly fix it? Thanks in advance, Poya