By the way, threw out mild oath (7)
I believe the answer is:
strewth
'mild oath' is the definition.
(I've seen this before)
'by the way threw out' is the wordplay.
'by the way' becomes 'st' (I've seen this in other clues).
'out' indicates anagramming the letters (out can mean wrong or inaccurate).
'threw' is an anagram of 'rewth'.
'st'+'rewth'='STREWTH'
(Other definitions for strewth that I've seen before include "mild oath" , "blimey" , "Mild expletive" , "Antipodean exclamation" , "Expression of surprise" .)