Here is a quick and dirty guide to some internal and external egg quality issues. Most of these eggs would be detected and removed at the grading station before they ever get to the grocery store. Still, it's pretty interesting to see all the different things that can go wrong with eggs!
Internal egg quality
Double Yolked Eggs: Two ova (yolks) are ovulated at the same time and travel down the reproductive tract together, and the shell forms around both.
Blood spots: This is relatively rare and occurs when a tiny blood vessel ruptures when the yolk is being released into the reproductive tract. Blood spots are usually very close to the yolk and the eggs are still edible. Blood spots do not indicate whether an egg is fertilized.
Meat spots: These spots are small pieces of tissue that are sloughed off of the oviduct and are absorbed into the developing egg. They can also be blood spots that have changed colour. They are usually associated with the albumen (egg white) and are not always detected during candling (unlike blood spots). They are also safe to eat or can be removed prior to cooking.
Runny egg whites: egg white is thin, watery and spreads out over a large area when egg is cracked open. Often seen when eggs are older, or eggs that are stored at high temperatures/low humidity levels
External shell quality
Cracked shells: Hair line cracks, star cracks, or large (also called "gross") cracks that result in a hole in the shell. May be caused by birds pecking at the eggs, "toe picking" or kicking the eggs, or from the eggs running into each other on the egg belt. Eggs can also become cracked as they make their way out of the barn at the transition between the egg belt and conveyors. Cracks are usually detected by a procedure called candling. This is when a light is held behind the egg and cracks become illuminated. Candling can even be done with an iPhone flashlight (see below)!
Body checked eggs: The shell of the egg is cracked while still being formed, so the hen repairs the shell before the egg is laid. This usually occurs because of some disturbance to the hen as she is forming the egg (below, left).
Wrinkled or corrugated eggs: The egg fails to plump up and the shell membranes are not fully stretched. The wrinkles in the shell become calcified (below, centre).
Slab-sided eggs: A second un-calcified egg enters the shell gland before the first calcified egg is laid, flattening its side as it is pressed against the egg in the shell gland (below, right).
Shell-less eggs: An egg that is laid prematurely, prior to shell formation. They may only the shell membrane formed before they are laid (below, left).
Thin egg shells: Eggs that are not completely calcified, or with an incomplete shell. This may indicate the secretory cells in the shell gland are not working properly (below, centre).
Pimpled eggs: Small lumps of calcified material are deposited on the egg shell. The severity of pimpling depends on the foreign material present during calcification (below, right).
Dusted eggs: Extra calcium has been laid down on the egg, likely because it has been in the shell gland too long. This is much easier to see on brown eggs than white (see below). One reason for this is when a hen holds on to her egg due to stress (e.g. being kicked out of the nest by another hen).
Egg within an egg: A fully formed egg moves from the shell gland back up the oviduct and a new egg (shell+ albumen, potentially yolk too) is formed around it.
Yolkless eggs: A piece of tissue is sloughed off from the reproductive tract and stimulates the oviduct to form an egg around it (albumen + shell).
Egg size: Egg size is dependent on yolk size. As a hen gets older, the yolk size increases. Usually, older hens lay larger eggs. Nutrition, genetics and management of the flock all affect bird size and therefore egg size.
Sources
Descriptions also adapted from "The Shell Egg: Formation through Processing Plant" a lecture given during the "National Egg Products School" by Dr. Kenneth E. Anderson