I'm a private pilot (Cessna 172 and Piper Cherokee). When there's a major outdoor sporting event, the FAA enacts a temporary flight restriction (TFR) extending for a several mile radius around the stadium. Since these facilities are almost always in major cities, radar coverage would be pretty good so there would be some warning time. While it's possible for someone to come in very low, it's hard to completely evade ATC radar. Do security personnel at the stadiums have anti-aircraft weapons? I honestly don't know, but if they did, the warning time would give then some time to respond.

TFRs are also enacted around high value targets such as nuclear power plants and also around presidential visits. The latter ones are especially difficult because they change so often.

Your garden variety Cessna or Piper could carry a few hundred pounds of explosives, enough to do a lot of damage. More dangerous planes would include crop dusters, larger single engined planes (e.g. Cessna 210), and twins like the Cessna 310 (or 400 series) or a Piper Navaho. They can carry much larger loads and they carry a lot of fuel, too. Gasoline can be as dangerous as explosives in some circumstances.

One concern is a false alarm that could lead to a fatal shootdown. This almost happened during the Reagan funeral in DC. A twin-engined plane (Beech King Air turboprop) carrying the governor of Kentucky suffered a transponder failure. Miscommunications between government agencies caused a mass evacuation of the Capital building. Reportedly, the plane was almost shot down.

The hearing came in response to the panic caused when a King Air carrying Kentucky Gov. Ernie Fletcher to Ronald Reagan's funeral suffered a transponder failure. Although the flight crew complied with its clearance and was talking to air traffic controllers, the FAA and security officials failed to talk to each other. The U.S. Capitol was evacuated, and according to an article in Thursday's Washington Post, military officials were moments away from shooting the governor's aircraft out of the sky.

"The pilots and the Air Traffic Organization followed all required in-flight procedures. But the communications breakdown within the federal government potentially imperiled the governor of Kentucky," Boyer said.

At the hearing, most of the members stressed that the problem was the lack of communication between government agencies. Mica called the breakdown "alarming and unacceptable."

Transponders are simple electronics devices that return a coded signal to ATC radar when the radar beam strikes the aircraft. Depending on the type of transponder, the coded information might by just a 4 digit octal code (Mode A), the 4 digit code and the aircraft's altitude (Mode C), or more sophisticated info including traffic avoidance (Mode S). Transponders can fail for a variety of reasons, including device failure or low voltage. I've had two electrical failures in my Cessna. One of the first indications was ATC asking me if my transponder was working. Believe me, when a plane's transponder code drops off the radar screen, people pay attention.