If you have a problem with someone on your team, have the conversation in private: IM, one-on-one email, face-to-face meeting, etc.
It’s a modern way to apply the advice Dale Carnegie gives in “Be a Leader: How to Change People Without Giving Offense or Arousing Resentment”:
Call attention to people’s mistakes indirectly…Let the other person save face…Praise the slightest improvement and praise every improvement. Be “hearty in your approbation and lavish in your praise.”
Related: A transaction makes a customer [SvN] discusses Carnegie’s suggestion that if you want to make someone your friend, you should ask them to do something for you.