The production staff seemed to do their research on military customs, uniforms, etc. Even the way the 'Marines' interacted at Nick's BBQ was pretty spot on. However, Nick was clearly 'promoted' to Gunnery Sergeant, what we usually call gunny if you're not a boot -new guy. Here we can see he is wearing the rank of a Gunnery Sergeant:rank. And here he is wearing the rank of Sergeant. The two 'rockers' below three stripes up indicate Gunnery Sergeant, which is one of the best ranks in the Marine Corps for an infantryman, or any Marine for that matter. I know Nick's a 'sniper' in the show, but he had to start out as a regular grunt, or at least go through Infantry Training Battalion -ITB. It's tough to explain why gunny is considered one of the best ranks. As a gunny you're usually the 'Company Gunny' of an infantry company. That means you're in charge of beans, bullets, and band aids. So you're basically the 'go to guy' for the Company Commander -God/CEO/- who will also go to you for strategic advice, since you've been around the block a couple times. It's not far fetched to assume that Nick was meritoriously promoted to Gunny from Sergeant. But he would not refer to himself as 'Sergeant,' i.e., when he was giving his good bye speech to the camera in the storage room, he said his rank was Sergeant. Rank is everything in the Corps, and when telling people your rank, you would give your SPECIFIC rank, not just say Sergeant. I'm just truly surprised that they got most of the little stuff correct, but the BIGGEST thing they could fuck up on, they did. Comic kind of related

TLDR; towards the end Nick wears Gunny chevrons, but still refers to himself as Sergeant. In the Marine Corps, Gunnery Sergeant != Sergeant. Marines refer to themselves as their specific rank, i.e., if I was a Lance Corporal, I wouldn't say I'm Corporal Brogan. Because that's not my rank, I haven't EARNED it. I'm a Lance Corporal, etc.