Fool that a pedant picks (3)
I believe the answer is:
nit
I believe this clue is a double definition.
'fool' is the first definition.
(both can mean a stupid person)
'that a pedant picks' is the second definition.
(nitpicking is pedantry)
(Other definitions for nit that I've seen before include "Egg; fool" , "Louse's egg; idiot" , "small egg" , "Louse; fool" , "Foolish person" .)