Mistake in supervision (9)
I believe the answer is:
oversight
I believe this clue is a double definition.
'mistake' is the first definition.
(oversight is a kind of mistake)
'supervision' is the second definition.
('oversight' can be a synonym of 'supervision')
'in' acts as a link.
(Other definitions for oversight that I've seen before include "Neglect" , "Lapse" , "Failure to notice - blunder" , "A failure to notice, an omission" , "Innocent mistake" .)