Mistake is seized on by extremely tiresome bully (9)
I believe the answer is:
terrorise
'extremely tiresome bully' is the definition.
'terrorise' can be an answer for 'bully' (terrorise can mean to bully or antagonise). I am unsure of the 'extremely tiresome' bit.
'mistake is seized on by' is the wordplay.
'mistake' becomes 'error' (synonyms).
'seized' means one lot of letters goes inside another.
'on by' becomes 'te' (I can't justify this - if you can you should give a lot more credence to this answer).
'error'+'is'='erroris'
'erroris' placed inside 'te' is 'TERRORISE'.
Can you help me to learn more?
(Other definitions for terrorise that I've seen before include "Frighten or menace like roisterer" , "Spook" , "generate fear" , "Frighten greatly" , "Panic" .)