Bill picked up in mistake for a bat! (3)
I believe the answer is:
tab
'bill' is the definition.
(tab is a kind of bill)
'picked up in mistake for a bat' is the wordplay.
'bat' anagrams to 'TAB'.
Though, I am not sure how this is indicated.
Can you help me to learn more?
(Other definitions for tab that I've seen before include "Tally at bar (colloq.)" , "Small flap - bill" , "Running bar bill" , "Kind of label for bat" , "Flap; illicit drug pill (slang)" .)