Mentioned that the arbiter had been mistaken (8)
I believe the answer is:
referred
'mentioned that the arbiter' is the definition.
I can't judge whether this definition defines the answer.
'been mistaken' is the wordplay.
'been' becomes 'ref' (I am not sure about this - if you are sure you should believe this answer much more).
'mistaken' becomes 'erred' ('err' can be a synonym of 'mistake').
'ref'+'erred'='REFERRED'
'had' acts as a link.
Can you help me to learn more?
(Other definitions for referred that I've seen before include "Brought up, mentioned" , "Directed for information or made mention" , "looked up" , "Alluded (to)" , "Adverted, cited" .)