In every prior episode, and future episodes, Olivia's duty weapon is a Glock 19. But for the scene where Lt. Rosten and Master Sgt. Pruitt are fighting Olivia is suddenly carrying a SIG Sauer P-226, which is done for the dramatic effect of Master Sgt. Pruitt hearing the sound of a hammer being cocked behind his head.
The victim, a U.S. Marine, is consistently referred to as going AWOL (Absent without leave). AWOL is an Army term. The Navy/Marine Corps term is "UA" (Unauthorized Absence).
Pruitt is the "sergeant that lost a stripe due to fraternizing with a lower ranking enlisted woman". Since he is now a Master Sergeant, it means that he was a Sergeant Major before losing the stripe. If a Sergeant Major, the highest ranking enlisted person in a unit, is found guilty of fraternizing, he would not only lose a stripe, he would be "retired" from the Marine Corp.
Olivia says that Pruitt was demoted because of someone four ranks below him. At the time of his demotion Pruitt was a Sergeant Major, which is six ranks above Crewes' rank of Corporal.
In the last scene, Master Sgt. Pruitt is wearing the green Alpha uniform, but the chevrons on it are the scarlet and gold chevrons of the dress blue uniform. The green Alpha uniform should have scarlet and green chevrons.
In the fight scene after she's pushed back into a picture breaking the glass attempting to break it up, Detective Benson cocks the hammer of a SIG-Sauer pistol while it was pointed into a subject's head at point blank range. NYPD officers are issued only DOA pistols with a 12 lb trigger pull. It's not possible to cock the hammer on a DOA pistol and have it function as a single action pistol. Detective Benson normally carries a Glock, not a SIG-Sauer.
Master Sergeant Pruitt was demoted for fraternization, meaning that before he was a Sergeant Major. As that rank usually takes at least 20 years to obtain it seems very unlikely that Pruitt held it seeing how he's in his 30's.
The rape and murder of an active duty Marine Corps officer would be investigated by NCIS (Naval Criminal Investigative Service) not the JAG office or even the NYPD, especially if the rapist/killer is also a Marine.
Detective Tutuola states that the Cobra attack helicopter has a crew of two pilots plus a door gunner. The Cobra is crewed by one pilot and one weapons officer. Tutuola, a former ranger, would not make such an obvious mistake.