ODA food inspectors routinely check for proper refrigeration and holding of eggs at grocery stores and warehouses. Once purchased, the eggs should be inspected by the consumer for any cracks, checks, or dirt spots. If any are found, the egg should be discarded. All eggs need to get into the home refrigerator as soon as possible after leaving the grocery store. When eggs are properly cooked there shouldn't be a problem.
Refrigeration is a safeguard.
Whether handling raw hamburger, a fresh egg, or just about any other food product, proper hand washing is a must. The eggs themselves don't need to be washed since that should be done by the producers themselves. But again, a visual inspection of the egg should detect any defects. For Easter, the egg is usually hard boiled and ends up as part of a child's Easter egg hunt. Such eggs make for much fun but probably not for good food.