I write a lot of military nonfiction, so I see a lot of tropes regarding active duty troops and veterans in pop culture and even in the news media that don't jibe with reality, but do annoy me.
The veteran as always white, Christian fundamentalist, right-wing, racist, and LGBT-phobic. That only describes a tiny minority, actually. And it is kind of racist, homophobic, and sexist to never acknowledge the racial minorities, LGBT's, and especially the women who've served.
The veteran as blindly super-patriotic.. I don't know any who fit that description. All US vets have taken an oath to defend the Constitution. Most take that oath very seriously. And most I've known complain very vociferously about any politician they see as not doing their part.
Veterans as all "damaged goods" whose PTSD makes them violent criminals. As someone with PTSD and as a caregiver for others with PTSD, that one full-on ticks me off. First off, a lot of veterans go their entire military careers without witnessing or experiencing any critical stress incidents. Of those who do, maybe a fifth of them develop PTSD. And of those with PTSD, only a statistically insignificant minority commits violence against others as a result.
There are some gun-related tropes I particularly dislike. The "warning shot," infinite capacity magazines, MC's proving they're badass by spraying ammo everywhere, and "it just went off" all show that the author hasn't spent a second researching firearms and their safe handling.
There are a few Damsel in Distress variations I particularly loathe. The hero's female love interest standing there and watching while the hero and villain fight over her is one. It's almost worse when she makes an effort to help the hero fight the villain, but because it's only a token effort, it doesn't accomplish anything except make the (usually male) writer believe he's got some feminist ally credibility.