The vegetables are mostly lettuce however I have given them apples and radishes and various other plants. I've found they really go for the greens though. As for mold, etc., most of the stuff is the outer layer of cabbage/lettuce that has some brown spots or is just a little too old to be sold...
I recently scored with a local supermarket. I found they put their not-so-perfect vegetable in trash bags and then throw them in the dumpster in the back. I have been dumpster diving and picking out the vegetable and giving it too the chickens. My concern is that the chickens may be eating too...