Make a mistake with assignment (6)
I believe the answer is:
Here is my best explanation:
'assignment' is the definition.
'make a mistake with' is the subsidiary indication.
'make a mistake' becomes 'err' ('err' can be a synonym of 'make a mistake').
'with' becomes 'and'.
(Other definitions for errand that I've seen before include "A short journey to deliver orget goods", "Short trip with a mission", "Short journey to carry message for Renard", "Useful journey", "Short trip for a message", "Task involving trip", "Short assignment", "Native of a former German kingdom", "Message trip" and "Journey made on someone else's behalf".)