I have been a Police Officer and a School Principal.
As a police officer I saw the devestation that the accusation alone could cause. So point one is there should be a full, frank and fair investigation. Being registered as a sexual offender will do two things, one is to keep the offender away from the obvious areas of reoffending (like any job to do with children). The second is that, if the behaviour was predatory (not just situational) it will simply go deeper underground.
As a Principal, I want any one in my employ away from the school, permanently, and not in any situation that will allow reoffending.
On balance, dismissal is not enough. At root, any sexual harassment is about power. Misuse of power is not a 'mistake' it is a choice. Remove the offender from the opportunity to reoffend, unless he/she is willing to undergo significant therapy.
The trust is gone.