I think arming anyone on a flight is false security. The solution for me is an impenetrable cockpit door and some sort of knockout gas for the cabin (I have no idea if the latter is feasible). To make the reinforced door idea work, you would have to re-educate ALL pilots in the idea that, if the terrorists get into the cockpit, there is a very real possibility that your aircraft will be used as a weapon. This means you must ignore the screams from behind you and land your plane immediately. Sure, easy to say, but now that the civilian aircraft is a potential weapon, I don't think there's much choice.
As for security screening, anyone, ANYONE, that wants to get to aircraft MUST be checked. I don't care if it's TJ himself, once you eliminate a source for weapons to be taken on board, there is no need to put one on for them.