Every employer has had an employee that is a "troublemaker." Though the compulsion to fire this problem employee is great, it may be illegal to actually do so. OSHA's anti-retaliation provision prohibits retaliations against an employee who exercises safety or health concerns, and some states have a "whistle-blower" statute which protects employees from discharge or other retaliation if they report violations of law by their employer.
Before dismissing a "troublemaker" or taking retaliatory action, seek out information about the complainers, find out information about the complaint, and try to resolve the complaint. Never act hastily.