Don't assume that data sets that you receive from clients have already been through any form of compliance testing, because the burden of responsibility lies with you and no one else. If you have any doubt about compliance testing, you need to do it again and be able to provide an audit trail.
Compliance rules vary by country, and a good starting point for understanding what you need to do is to check out the Direct Marketing Association in the country in which you operate. The specific elements to check also vary by country, but a number of them are common: permission to contact by mail, email, and telephone are perhaps the most important. You need to check your data against frequently updated lists, usually on a monthly basis. It's a good discipline to dedicate a CRM field to the date of checking along with an audit trail showing when it has been done and by whom, and when the results returned.
When purchasing data for use in campaigns, don't assume that it has current or indeed any compliance testing. Again, the responsibility rests entirely with you as the data user.