distinction
The show achieved the dubious distinction of becoming the fastest-closing London musical in recent times.
The region has the dubious distinction of having the highest rate of asthma in the country.
Ruth Ellis has the dubious distinction of being the last woman to be hanged in Britain.
We have the highest rate of car theft in the country - it's a dubious distinction.

SMART Vocabulary: related words and phrases

Reputation
by reputationidiom
cred
credibility
detoxify
disreputable
honourable
honourably
infamous
infamously
infamy
mud
notoriety
notorious
notoriously
reputable
reputably
smoke
stature
Teflon
there's no smoke without fireidiom