How does a Game of Thrones "mishandle morality"? In my opinion, the shows (and books) present human morality more realistically than any other fiction I've ever seen
It mishandles it because some signals that set certain characters up as the good guys that we should route for are in conflict with actions they take which destroy some of our sympathy for them, indicating that the writers didn't really think through the moral implications of those actions, brushing them off too lightly.
For instance, when the butcher boy is killed, Stark looks mildly perturbed but doesn't protest about it, and is still willing to throw his lot in with the despicable Lannisters. It's mostly shrugged off, but the incident was far too dark for that. Or another example, Robb Stark sacrificing two thousand soldiers on a suicide mission which was a strategic feint. Although one can see how the tactic might work, it just makes no sense on a human scale, unless you buy into that glorious death-in-battle nonsense big time (on a Kling-on scale it would be ok).
For instance, when the butcher boy is killed, Stark looks mildly perturbed but doesn't protest about it, and is still willing to throw his lot in with the despicable Lannisters. It's mostly shrugged off, but the incident was far too dark for that. Or another example, Robb Stark sacrificing two thousand soldiers on a suicide mission which was a strategic feint. Although one can see how the tactic might work, it just makes no sense on a human scale, unless you buy into that glorious death-in-battle nonsense big time (on a Kling-on scale it would be ok).