Broad-minded, but not alert, unfortunately (8)
I believe the answer is:
tolerant
'broad-minded' is the definition.
(similar in meaning)
'not alert unfortunately' is the wordplay.
'unfortunately' is an anagram indicator (a bad or unfortunate spelling).
'not'+'alert'='notalert'
'notalert' with letters rearranged gives 'TOLERANT'.
'but' is the link.
(Other definitions for tolerant that I've seen before include "Showing respect for the opinions of others" , "Showing leniency" , "Indulgent, permissive" , "Showing respect for the rights of others" , "Willing to allow others their opinions" .)