Unpleasant quality of inn's seats wobbling about (9)
I believe the answer is:
nastiness
'unpleasant quality' is the definition.
'inn's seats wobbling about' is the wordplay.
'wobbling about' is an anagram indicator.
'inns'+'seats'='innsseats'
'innsseats' is an anagram of 'NASTINESS'.
'of' acts as a link.
(Other definitions for nastiness that I've seen before include "Pollution" , "Repugnant behaviour" , "hostility" , "Malevolence" , "ill humour" .)