You Don't Always Have to Solve Conflicts Immediately
The pair began to argue, with their argument gradually escalating into four-letter words and such. Meanwhile, several customers watched, embarrassed, while the conflict brewed on and on. The manager told the employees (in front of everyone) that he would need to work out the argument with them tomorrow.
This problem didn't need to spill over into customer service the way it did. The manager could have sent one or both of the employees home, or at least on a sabbatical for an hour or two, and then worked with them to solve the disagreement when tempers weren't flaring.
Conflict management isn't an exact science, and among other things, it can vary greatly by industry. But this serves as a nice reminder that sometimes problems are best solved when other employees, and customers, are not present.