Hah, managing people is probably one of the toughest things to do. The reasons varies but a key component is that emotions/feelings comes into play which means that most folks tend to have an emotional investment in their work.
Anyhow, I got to deal with a people issue where one team member decided to trash another while the other employee is away. It was a comment (unfortunately it wasn't one-off as this employee has repeated it a number of times at different occassions). Regardless whether it's true or not, I will have to have a little chat with said employee and request that he stop doing that and to respect all team members. Maybe I should have stepped right in and told him that during the team meeting but I didn't think it would be appropriate to kind of jump down his throat.
I guessed the next best thing is the little chat and see how it goes from there.