Make a mistake with mission (6)
I believe the answer is:
errand
'mission' is the definition.
(I've seen this before)
'make a mistake with' is the wordplay.
'make a mistake' becomes 'err' (to err is to make an error).
'with' becomes 'and'.
'err'+'and'='ERRAND'
(Other definitions for errand that I've seen before include "Commission, message" , "Messenger's job" , "Job usually involving a short trip" , "Journey to deliver message etc" , "Useful journey" .)