At the fruitstands, I sometimes see, especially oranges and green peppers, with white stains on them. What are these stains? Are they pestisides, which render the produce unhealthy for consumption?

I believe that is wax. Fruit is washed when it is picked (to remove pesticides and dirt). The washing also removes some of the fuit's natural wax (this wax helps keep them from drying out), so it's common to coat them with wax after washing so that they last longer and look better. The FDA approves these waxes as safe to eat, but (if you are concerned) they can usually be removed fairly well by washing, and there are products that claim to do a better job.

Insect feeding on some fruits, especially tomatoes, will result in discolorations that look like white spots. You may see a tiny pinhole at the center of the spots as evidence. Though this sounds bad, these fruits are quite safe for consumption.

methos: I have seen cucumbers which look waxed. I eat cucumbers with their skins. So if I sound slippery. . . .

coldfuse: I have seen kiwis which have pin holes. I eat kiwis with their skins. So if I sound mousy. . . .

I am referring more to small white stains, which do make the fruit appear as though they were washed but not rinsed well. These small white stains remind me of those old Cascade commercials in which the "other" brands of dishwashing liquid left such spots on glasses.

If by small, you mean spot-like, I'd go with Fuse's explanation. Your description of a residue like a soap residue makes me think that my guess was correct. Ideally, the wax is spread evenly and is clear, but in practice it can leave a residue.

I meant small but big enough to be blotchy. Here is one last associated question, if anyone knows the answer. Are the "blotchy" brown spots on peaches also harmless, or are they caused by pesticides or acid rain?

Those brown splotches are fungus infections and will rapidly destroy the fruit and can go on to infect the twigs and branches to which such infected fruit is attached.

Eating those spots are not recommended, but they can be cut out in a very early manifestation before the fruit has been fouled totally.

Sherasi: I am amused that you know about the health of fruit as well as humans.

Well, I don't know a lot about fruit or plants, but I am a darn good internet researcher!