Here's something most people who eat organic foods have probably never thought about. While organic produce is largely free of the harmful herbicides, pesticides and chemical fertilizers used to grow traditional crops, they do share one thing in common: the sticker. The stickers found on organic fruits and vegetables that identify them as being organic use adhesive glues that may be contaminating the food with compounds that are decidedly not organic.
Here's a link to the FDA code that shows what chemical compounds are allowed to be included in sticker resin:
A quick glance at the list reveals a number of chemicals deemed safe by the FDA that you probably don't want coming in contact with your organic produce. BHA, BHT, butyl rubber, petrolatum, polystyrene and rubber are all on the list, as are a number of petroleum byproducts and other chemical compounds.
Sure, the amount of chemicals the sticker leaches into a piece of fruit or a vegetable is going to be miniscule, but it's yet another contaminant I don't need or want in my food. People purchase organic products in order to avoid chemical contamination, so it borders on ludicrous they're allowed in the stickers that certify the foods.
Some of these compounds can be absorbed into the fruit or vegetable, so washing it may not get rid of all the residue. Your best bet is to grow your own produce or find a local source of organic produce that doesn't use stickers. Your local farmer's market or co-op may sell organic produce without stickers.