Sometimes an egg will get broken in the nest and a hen will discover how good they taste. Once she discovers this, she will look for broken eggs or break them herself. To eliminate this the hen must be located and removed from the flock. If this isn't possible, fill several eggs with tobasco or other hot pepper sauce and leave them for the hens to eat. This will sometimes will eliminate the problem. Correcting the things that could be causing the broken eggs is paramount. Not enough nests, inadequate bedding or not collecting eggs often enough are the leading causes.
Feather-picking and Cannibalism
Both are bad habits that can develop in the brooder and carry into laying. The exact cause is not always known. Poor nutrition, overcrowding, overheating, not enough feeder or water space, even lighting can be factors. At the first sign of picking, action needs to be taken to stop it. If bleeding starts, the birds can pick each other apart and the losses can be heavy. The problem sometimes can be corrected by providing more feed, water, or floorspace. Or maybe better ventilation, cut back on light or adding flakes of hay or greens for the birds to pick through. An anti-picking/anti-cannibalism agent can be applied to the affected birds as well, to promote healing and make the areas very bitter tasting to any birds pecking at it.
Mites are a very common problem with poultry. usually transmitted from wild animals in the area especially in the winter months. Around the vent area is the best place to spot them (thats the warmest part of the chicken) fold back the feathers and inspect the skin and feather base, look for small white/light brown bugs crawling around and possible brown/black clumps at the base of the feather which is were the mites lay their eggs. Mites are extremely easy to get rid of, two of the most common methods involve dusting the chicken and the coop with either a permethrin based poultry/garden dust or the more natural way of dusting with food grade Diatomaceous Earth (DE), the DE is safe enough to be sprinkling in nest boxes, all over the coop/run, and even in their feed as a anti-parasite agent.