When I render a clip with a few layers of color correction and or filters in FCP 4.5 it becomes grainy even if before I render it it looks fine.

Anyone know why this happens?

Thanks.

Without seeing the actual clip it's hard to say. However, I've seen something similar before. Prior to rendering you're seeing a low quality approximation of the clip. I think that noise can be lost in these because the resolution is low, but rendering shows all its flaws.

Color correction is tricky because, depending on what you do, it can bring out noise and also lead to banding (noticeable outlines in areas which should have smooth transitions from dark to light). So you may just be pushing your footage beyond that limit of DV25's colorspace.