Your company can be legally liable for negligent hiring if you fail to uncover a job applicant's incompetence or unfitness by checking their references, criminal records, or general background. You can be sued for negligent hiring for failure to become aware of an employee's unfitness for a particular position, or for subsequent failure to take any corrective action, such as training, reassignment, or discharge, to remedy the problem once you find out about it.
Particularly if you have employees who have or will have significant contact with the public, customers, patients, or children, you'll want to investigate these topics: