What's the worst that can happen from leaving a broken nose unfixed?

Shape and breathing. An untreated broken nose may be crooked and the breathing through the nose can be obstructed. These can usually be corrected later on with surgery. It is much simpler to set a broken nose soon after an injury however but this should be done within two weeks of an injury.
Broken nose. May have difficulty breathing or unsatisfactory cosmetic results. These can often be addressed down the line with surgery.
Deformity. You may have a bent nose, deviated septum, septal hematoma or abscess, or a saddle nose like a boxer.