The Inspectors 2: A Shred of Evidence.

Postal inspectors investigate a con man who uses the identities of others to falsify credit card purchases. Stealing credit card offers from mail boxes, he obtains cards in others' names, makes many purchases until the card is maxed out, but is always careful to pay minimum balances. According to the story, it is possible for individuals such as this to run many credit cards at a time without being caught.