It is "conduct unbecoming", to be sure. Would it increment to the conviction that Taliban members/sympathizers already have towards the foreign presence? I doubt it. As to whether it is conduct of the sort to diminish the moral authority of the American presence in Afghanistan, amongst those who do not currently side with the Taliban, I would say that it doesn't do so any more than the many incidents that have preceded it, or any moreso than the degree of corruption within the Afghan bureaucratic and political ranks does (which is, in turn, rightly or wrongly perceived by many to exist because of outside intervention). It certainly doesn't make people forget about Abu Graib. However, by virtue of its current high public profile, it certainly compromises the safety of any Americans who might fall into Taliban hands, and we should be concerned about that.
Fundamentally, though, the focus of the current ruckus seems to be primarily about convincing Americans that they always "do the right thing".
And just so we're clear, soldiers are also young men and are not immune to the stupidity of shooting videos of impulsive acts and posting them online. They could be young women hoisting their shirts at a drunken frat party, or they could be teenage boys trying a stupid skateboard stunt à la "Jackass", or they could be people in hoodies smashing Starbucks windows for media exposure at a G8 demonstration, but in this case they happened to be American soldiers who successfully killed their enemy. And like so many idiots within present day society, they felt that "the cake needed a little icing", by doing something outrageous for the camera.