For example, much is made of the fact that real-life Special Forces soldiers aid in the development of these games for the sake of authenticity. That's great, but that authenticity is then baked into products that paint a wholly misleading picture about the realities of war. The Medal of Honor franchise is also guilty of this.
In a much larger sense, it just feels like there's a giant entertainment industry cash grab that's been taking place off of ongoing US conflicts, and it's being masked in soldier worship and flag-waving. In my opinion, this phenomenon only serves to obscure the real sacrifices made by service personnel.
This is even more unfortunate when you consider the franchise is heavily marketed on the basis of its supposed authenticity, and its main audience tends to be quite a few years below each game's M rating. I don't even remotely care about violence in videogames, but messaging that resembles propaganda seems troublesome, especially with a younger audience.
That said, I realize they're games, and the object of games is to entertain. Therein lies the second problem: Call of Duty games tend to be mediocre at best. The fact their sales are so strong is a testament to Activision's marketing powerhouse.