For an offence of Common Assault to be made out there is no need for physical injury to have occurred. In fact there is no need even for physical contact to have taken place. If injuries that need the attention of a doctor have been inflicted it is likely that a more serious charge will be preferred.
If the alleged victim of Common Assault maintains that they have been injured it may add to the strength of their evidence if there are, say, photos of their injuries. However it is by no means essential and most Common Assault cases presented to court do not include such evidence.
You do not give much detail of the incident you mention but if a person was injured accidentally by the pot being dropped a charge of common assault will not succeed.