I await Boogie's opinion 
oh, allright, I'll oblige.
First vid: I would have a very hard time justifying a direct punch to the face of a woman. Especially one, who, judging from the vid, is not combative. That being said, there would be circumstances where strong measures can be justified against a woman. My self-defence instructor at the academy said that the most difficult fight he had been in on the job was trying to subdue and control a 110lbs coked-out naked woman. edit: And this was a man who was 6'2", 220lbs, and is the scariest, most intimidating motherfucker I've ever met. And since I've trained with professional MMA fighters, that's saying something.
So, gut reaction: the punch wasn't necessary, everything else was kosher.
Second vid: I see nothing at all wrong with the officers' response.
The major difference between the two, as FatalT referred to, is the number of officers present. There is a HUUUUUUGE difference in responding as a single officer on scene, as opposed to having two or three officers as backup. It
completely changes the nature of the situation.
and just as an aside on the second vid: it is
incredibly difficult to arrest an individual who is dedicated and determined to resisting arrest, even in a two-on-one situation. You simply have no idea. In the theoretical sense, I'd take the dude down hard and use my martial arts training to subdue him. But, and this is not intended to be boastful, my martial arts training is
far superior to the average cop's skills, so I cannot expect them to react as I might to a situation.
edit: Actually, the guy in the white T-shirt who confronts the cop at 5:45-6:00, despite not knowing what he's saying....at that moment, I might be fucking him up. The cop walking away, and the punk following behind him, depending on other contextual factors, that's combative behaviour, and believe me, that punk would regret it.
