In addition to checking each name for conflicts of interest, you should also check each name for prior legal involvement (both criminal and civil). A previous order of protection against the person, or a prior conviction for a violent offense, should raise a red flag. In Arizona, most court records are available here, though the records are not complete and local courts may also require checking.
Finally, you may wish to screen the client for indicators of domestic violence, particularly in a domestic relations/family law practice. Even if the domestic partner is not the opposing party, an abusive partner can easily become violent towards the attorney if he is unhappy with the case. The Center for Relationship Abuse Awareness has prepared a useful interviewing tool that can be found here. The American Bar Association also has some very useful information and guidance here.