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Have you had a lot of rain, or have you watered and got the leaves wet frequently? If so, your white spots might be powdery mildew. It could also be an infestation of mealy bugs, they resemble white powder sometimes, although I would not describe it as "spots".
shawn47 - Yes. Melons require more water than some other vegetables, but you should still keep the water off the leaves.
Melons, squash, and cucumbers are rather susceptible to powdery mildew. I used to live in South Florida and could never get them to grow there. I have the reverse here. It rains very little in the summer, and have more squash than we can possibly eat!