Here's a tip: Use a grapefruit spoon ($2, Broadway Panhandler) to pull out those pieces of eggshell. The serrated sides of a grapefruit spoon cut through the viscous whites while the elongated bowl of the spoon makes it easier to target that frustrating speck of eggshell.
We frown at single use tools here -- as reader Chzplz pointed out -- so I'm happy to find use for the handsome grapefruit spoon beyond Broiled Grapefruit breakfasts. For another egg tip, check out our How to Hard Boil an Egg.
Do you crack the eggs into a small bowl before adding eggs to the mix? This can seem like a slow step and creates one more bowl to wash. But, this way one bad egg won't ruin everything. Also, it is much easier to grapefruit-spoon out pieces of shell in a small bowl.