Summer squash can be susceptible to some insect feeding like cucumber beetle, squash bugs, powdery mildew, etc. See our vegetable profile for more information and common problems. http://extension.umd.edu/growit/vegetable-profiles-summer-squash
We cannot say what the white spots are. Your zucchini may have some scarring and insect feeding. If laying on the ground they may have some rasping by insects. They are okay to eat. Peel damaged sections.
Do not let the fruit get too large. Harvest when the squash is still immature, only about 6- to 8-inches long and 1½ to 2 inches in diameter for elongated types. If the rind is too hard to be marked by the thumbnail, it is over-mature. Remove old fruit to allow new fruit to develop. Check plants daily once they begin to bear fruit.