It doesn't bother me in the least that Cullen is to be the military adviser. I see some people think Loghain or Aveline would have made a better choice, but I'll have to disagree. While I love both characters, I see no reason why the Inquisitor would know them--or Cullen for that matter. Knowing Cassandra is the one who chose the military adviser, I would assume from what she knows would be limited on them, as well. She may know Loghain or know of him, but perhaps in her view, he is a general past his prime. A man who went boldly against his king's orders, causing the death of nearly the entire Fereldan order of Wardens, and nearly the King's entire army. She may know that he then helped sell elves into slavery, backed a man who killed an entire keep of people, including a powerful family second only to the king, and then allowed his daughter to be imprisoned. Now, again, no hate towards Loghain (I love him, actually), but that is certainly a possible projected image of him. Perhaps he isn't even around for her to hire him. At this point, no one knows the circumstances of her bringing Cullen on.
Same with Aveline. I am not sure why Cassandra would single her out to be an adviser. She was a captain of the guard. While professionally trained, I wouldn't call them an army by any means--just as I wouldn't call my local police department an army. Again, maybe Aveline wasn't even around. I would be surprised that at the time the Inquisition was formed, an abundance of choices would be available, considering thousands died. I don't imagine there was a resume service set up and Cassandra was holding auditions. No one knows because the game isn't even out.
I would assume templar's have some sort of military training, considering they are a military order. They are trained to deal with demons and since they're raining from the sky at the moment, I would think having someone who is not only trained in the ways of military order, but trained in combating demons--a very good option. If she saw him commanding the remaining templars in Kirkwall, saw them respect him, saw them ready to follow his orders, saw how he lead them, he may have been an easy choice for her. Instead of seeing him as a templar who made mistakes, she may see him as someone who struggled between his duty and his belief, made some mistakes and grew stronger because of them. /shrugs
Not to mention, my little dalish elf knew nothing of leading an army or warfare. Yet, she became a Grey Warden, united an entire country under the Warden's banner, won a Landsmeet, placed a king on the throne and was personally chosen to lead his armies against the darkspawn. She did okay.
At the end of the day, it's speculation. As it will be until the game is being played and the story being told. As of now, I am willing to wait and see how it plays out before gaining a notion that anyone can or cannot do something. It's some good advice to follow.