In general, the episode title "Stolen Valor" refers to the impersonation of military personnel in order defraud and extract some sort of benefit from another. Federal law states that it is a misdemeanor if convicted, especially if once claims to have received military honors in order to receive said benefit, Stolen Valor Act of 2013.
Whistler goes undercover as a Canadian; actress Tori Anderson is Canadian.
The Defense Enrollment Eligibility Reporting System (DEERS) database contains information for each Uniformed Service member (Active Duty, retired, or a member of a Reserve Component), US-sponsored foreign military, DoD (Department of Defense) and Uniformed Services civilians, other personnel as directed by the DoD (including the patient population serviced through the Military Health Services System), and their eligible family members.
CAC is short for Common Access Card, or more informally known as an ID, or Identification Card. With said card, you can access secure rooms through a proximity card reader and access government databases which require authentication by an attached reader to computing device.
NEX is short for Naval Exchange, or the Base store.