Mistake, foreman not finishing (5)
I believe the answer is:
gaffe
'mistake' is the definition.
(gaffe is a kind of mistake)
'foreman not finishing' is the wordplay.
'foreman' becomes 'gaffer' ('gaffer' can be a synonym of 'foreman').
'not finishing' means to remove the last letter.
'gaffer' with its final letter removed is 'GAFFE'.
(Other definitions for gaffe that I've seen before include "Brick (that's dropped)" , "bad mistake" , "Clanger" , "A blunder, faux pas" , "Tactless remark" .)