Wizofoz has it right.
Often one of the first indications will the air going supersonic over the cockpit roof, creating a local shock and breaking laminar flow. This can be clearly heard as a pretty loud rumble and felt as a shaking of the aircraft.
If you get local shocks in the vincinity of control surfaces, youre in for a very nasty surprise: this means controls become ineffective, or even that the control effects are reversed!
This does not happen easily on airliners, though, and you would have to be a complete idiot to deliberately push one that far.
Airliners have gone supersonic after failures and survived though, notably a 727 which went into a spin and then a vertical dive, and I believe the China Airlines 747SP which took a spin-dive over the pacific. Both lost bits and pieces, but both managed to land after the gears got extentded by g-forces and slowed the aircraft. Wet pants all 'round.
regards, OORW