That said I have yet to see the streaks you have described in my own D300s. By way of an experiment I took two of my polariser filters and inserted the Nikon screen protector in between them. Instantly I see beautiful rainbow stress patterns which perhaps are similar to the effect you have seen.
(As a side note if you are every using two polariser filters together to produce a neutral density effect then you need to ensure that if one of the polarisiers is a linear type then it must be the one furthest away)
I'm not suggesting that you have been viewing through the protector (or the throw-away film across the actual screen) just that the effect may be coming from the internal sandwich of plastic layers one of which is likely to be a polarising layer.