Although we rarely find a bad egg these days, always separate egg whites into a smaller cup before adding to the rest. You will eliminate problems like bits of shell or specks of yolk that can ruin the whites for things like meringue.
Hard boiled egg whites do not freeze well. If you plan to freeze a recipe that contains hard boiled eggs, leave them out while freezing and stir into the thawed dish when possible.
Place eggs in a sauce pan and THEN cover with cold water. Bring the water to a full boil, cover pan, remove from heat, and let stand for 18 to 20 minutes. Pour off hot water, then shake eggs in covered pan to crack the shells. Cover the eggs with ice or run cold tap water over the eggs to cool, then peel.
If you plan to make deviled eggs, turn the eggs over in their carton the night before. The yolks will center themselves, eliminating the lopsided egg that tries to tear on a thin end.
Never put egg shells down the disposal if you are on a septic tank. Throw them in the trash or use them in your compost instead.