Robb Willer argues that telling others about liars is useful gossip and shouldn't be condemned.
We've been doing research for several years about the ways in which reputational concerns encourage people to behave. This led us to get interested in gossip because gossip involves diffusing reputational information about people in groups. More specifically, we were interested in an apparent tension between the bad reputation gossiping and gossipers have, but how there's a lot of ways gossip has useful social functions.
We found people very readily warned the next person, passing on socially useful information to them. But what was more interesting was the emotional register of the behaviour. As people saw a person behave in a untrustworthy way, they became frustrated and their heart rate increased. But when they had the opportunity to pass a warning on, that reduced or eliminated their frustration and also tempered their increased heart rate.
It is a subset of gossip that involves warning other people about untrustworthy others. We think it is pretty common. We find generous people are more likely to engage in it and they report doing so out of a motivation to help others. It is very different from malicious gossip, which might be driven by a desire to tarnish another's reputation or advance oneself.
The Bible certainly condemns liars and lying, but is identifying a person as dishonest a proscribed form of gossip? I'd say no, as long as the revelation itself isn't done for malicious or deceitful purposes.
Proverbs 11:13 says "A gossip betrays a confidence, but a trustworthy person keeps a secret."