I watch a lot of television, movies, trailers, and trailer breakdowns for work, but here's the thing: I can't tell you or anyone else what makes a genuinely good military movie or show, especially if I haven't seen it yet. And I wouldn't call myself a "critic" in the classic sense. Then again what do they know; they said The Hurt Locker was a masterpiece.
What I do know, is that I get excited about stories that make an honest effort to achieve some measure of authenticity, whether it's a full blown dramatic reenactment of some major conflict, or seeing characters interact (even briefly) in a way you recognize, because you've had those conversations on base, overseas, or while you were drunk at one in the morning in the barracks.
At their best, military movies and shows focus on a character's service as more than a lazy plot device to explain why they're good with guns, have a high and tight, or shout out bits of military lingo at random moments; at their very worst, they may trot out the broken vet trope to add a little drama. And of course, there's the laziest of them where everyone's an operator — even lawyers, apparently.