bsp tree issue

I have been working on a project recently that requires building a bsp tree from a list of polys and displaying the scene using OpenGL. I only send through triangles. There are only simple geometric objects in the scene. Of course, there were a lot of bugs when I started, but I fixed all of them... except for one. The objects display fine when using the z-buffer and sending all the polys through in no particular order. But, when I turn z-buffering off, and render the scene by traversing the bsp tree in the correct fashion with just backface culling a minor issue pops up. Everything is fine except there are small black dots (mainly), and tiny black polys (rare) that pop up on the objects as I move the camera around. They pop up and go away as the camera moves. This is my first use of a bsp tree. I have tried to narrow down what the issue is, but I can''t figure this one out at all. I know other people working on the same project with me are having the same issue, and they don''t know what it is either. I''m sure someone on here has run into this, and hopefully figured it out finally. I''d be extremely grateful for any help on this minor bug. Thanks, G