1) I'm not saying that they don't exist, but I've never seen a plastic UV or protector filter -- they are always glass.
2) Take a look at the following post in this thread:
http://photo.net/nikon-camera-forum/00UNFa?start=30
Shun is a superb technician who I highly respect. Several years ago, he did a test that should put this "debate" to rest once and for all, at least for filters of any reasonable quality and for focal lengths under 200 mm: He stacked several filters in front of a very high quality lens and saw no effect.
If you are shooting with a really long, high quality lens, into the sun, and without a lens shade, you might see loss of resolution or increased flare with a cheap UV filter, but in other situations you're likely to be fine unless you shop for filters at the bottom of the trash bin.
FWIW, every photo that I have ever published (or posted here) has been taken through a UV or clear filter. No one has *ever* complained about lack of sharpness or loss of contrast in my images.
Tom M
PS - I forgot to mention that over the years, I have repeated Shun's experiment with several of my own lenses and obtained exactly the same result. If anyone doesn't believe this, doing a test like Hershey did takes seconds and answers the question unequivocally for their particular equipment and technique.