The term 'by mistake' can be defined by the crossword solutions of ERROR (5 letters), SLIP (4 letters), ACCIDENTALLY (12 letters), ERRONEOUSLY (11 letters), and inerror (7 letters). ERROR is an act or statement that is not correct, while a SLIP is an unintentional mistake. ACCIDENTALLY and ERRONEOUSLY both mean unintentionally, but ACCIDENTALLY implies a lack of awareness or carelessness, while ERRONEOUSLY implies a mistake due to incorrect information or reasoning. Inerror is a more formal way of saying 'by mistake'. All of these words refer to an action or statement that was done or said unintentionally.