"Shut up!" Bill's back interrupting nitpicker (6)
I believe the answer is:
pedant
'nitpicker' is the definition.
(I've seen this before)
'shut up bill's back interrupting' is the wordplay.
'shut up' becomes 'pent' (synonyms).
'bill' becomes 'ad' (advertisement stuck on wall).
'back' says the letters should be written in reverse.
'interrupting' is an insertion indicator.
'ad' reversed gives 'da'.
'pent' going around 'da' is 'PEDANT'.
(Other definitions for pedant that I've seen before include "Stickler for the rules" , "Academic stickler" , "One particular" , "One excessively concerned with minor detail" , "One who insists on minor details, may be a conceited know-all" .)