When the military CAC card is viewed of the veterans, it shows that the Pay-grade is E-5, Under the rank, PO2. In the Army, E-5 is the rank of a sergeant so under the rank, it would be SGT, In the Navy, an E-5 is a Petty Officer Second Class(PO2).
"Former Master Sergeant" (MSG) Sam Latimer is wearing Private First Class (PFC) rank in his ID photo. MSG Latimer is likely to be retired, so he would have an entirely different ID card.
Near the beginning of the episode, Reese mentions that Joey had recently returned from a deployment to Afghanistan and that his fiancée, Pia, had waited 6 years for him while he was deployed. Combat deployments last 18 months at the most. Military enlistments are generally 4 years active duty, and 4 years inactive duty (such as Reserve or National Guard), but can be 5&3, 6&2, etc. He likely was sent to a duty location at an Army post (being "stationed"), deployed, returned to his duty location, and then processed out of the Army. Civilians don't necessarily understand the difference between being stationed somewhere and being deployed, especially if they are stationed overseas (i.e. Germany or Korea).
When Joey is looking for the specific box, he says "H-7-3-3-3-6" (it sounds like 8-7-3-3-3-6), but he would actually say "hotel-7-3-3-3-6." Military personnel get so indoctrinated to using the phonetic alphabet, especially around other military personnel, that anything else sounds awkward.