I would spray them with an insecticide. I use the Garden Safe brand and have had good results with it. No...it didn't kill my butterflies and bees. We have tons of them!

Flowers will often get spotted from insecticides and even spray liquid fertilizer if mixed a little too strong.
The answer to an unknown problem is never spray with something. If you see bugs, then spray, but if the petals are spotted because of something you already put on them, more spraying will make it worse.
Look for the cause before you shot-gun solutions at it.
Linda C

Shasta Daisies are pretty tough plants. I spray mine and never have problems with them. If you see thrips, just spray the stuff on them and kill those suckers!

I second identifying the problem before spraying. If it is thrips, there are several really helpful posts that will give you some ideas on dealing with them. If your interested in using organic methods, there is a really informative post in the organic gardening forum. Doing a search will turn up several threads.

For your sake, I hope it's something else. Thrips can be the devil!