sorry to bring up an old thread but i think my input is relevant and not worth starting a new thread.......
i have been experiencing the same muffled popping/rumble sound then shaking when car is idling after cold start. i noticed the rumble and shaking start to settle down after the engine oil had warmed up to about 90 degrees.
couldn't figure out what was wrong, then 2 weeks later the check engine light came. it turned out an exhaust leak at the rear muffler was causing the rumble and shake while idling.
the leak was at the weld joints along the exhaust pipe that had started to rust. this was probably making the car run a little too rich as well, but i could be wrong.