Make a mistake and trip (6)
I believe the answer is:
Here is my best explanation:
'trip' is the definition.
(errand is a kind of trip)
'make a mistake and' is the wordplay.
'make a mistake' becomes 'err' ('err' can be a synonym of 'make a mistake').
(Other definitions for errand that I've seen before include "Short commission", "Short journey to get or bring", "Short trip with a mission", "Ran red (anag)", "Short trip for a message", "An ...... of mercy is a journey to relieve distress", "Messenger's job", "short shopping trip", "Charge - mission" and "run one".)