Frankly, despite Al Jazeera playing the video clip non stop, I don't think this incident will make a damn bit of difference. In fact, it may even help us.
We went into Fallujah guns blazing, blasting houses, mosques, shops, etc. We probably killed over 1000 insurgents, and there obviously were civilian casualties as well. IOW...the controversy over the battle itself dwarfs whether we shot that one wounded insurgent.
I can't really imagine someone who supported the attack in Fallujah, with all the death and destruction it wrought, suddenly switching sides because we shot one wounded insurgent who we might easily have killed the first time through anyway (although Doc Mercer would love to pretend that is the case). Likewise...for all those people already taking up arms against us, they already hate us, and engage in kidnappings, mutilations, and head-lopping that dwarf this. This is incredibly small potatoes because he's the type of bad guy we were trying to kill anyway. And the really important thing is that he was <!--EZCODE ITALIC START-->not<!--EZCODE ITALIC END--> an innocent. That's what makes all the difference in the world in terms of the effect on hearts and minds.
And like I said, it might help us. Al Zarqawi said we'd lose in Fallujah; he was wrong. And apparently...a lot of those insurgents skedaddled because they didn't want to get crushed. It was the stupid/fanatical ones left behind. This incident now tells those insurgents still resisting that we can be brutal bastards too. We bring inevitable death with us when we fight. That may be some little extra bit of discouragement for those insurgents who wavering as to whether they truly want to fight this thing out.
Be nice, and we're nice to you. Be nasty...and you will be utterly brutalized. That's how you suppress an insurgency.