Demonstrated who's mistakenly used the second half (6)
I believe the answer is:
showed
'demonstrated' is the definition.
('show' can be a synonym of 'demonstrate')
'who's mistakenly used the second half' is the wordplay.
'mistakenly' is an anagram indicator.
'the second half' indicates taking half.
'used' halved is 'ed'.
'whos' anagrammed gives 'show'.
'show'+'ed'='SHOWED'
(Other definitions for showed that I've seen before include "presented" , "Demonstrated or depicted" , "Demonstrated or displayed" .)