dust definitely can get to the shutter and does quite quickly. remember inthe film days, as the camera was wound, the film would go out through a piece of felt-like material to clean the film on the way out and on the way back into the canister. also, each picture was a different piece of film. but you still could get dust on the negs prior to exposure.
with todays's dSLRs, you don't have any dusting mechanism, it's the same piece of 'film' for every shot, it has a slight charge to it so it's very dust attractive, the shutter curtains open for every exposure, and when the mirror slaps down, it tends to swirl around any dust that has 'settled' inside bahind the lens. so what often happens is during a series of shots, you can find a speck of dust or two on the sensor.
i use a squeezy ball to dust off my sensor often. and whenever i get dust that doesn't blow off or tiny drops of oil from the shutter (that happens quite a bit over time, too), i use a sensor cleaning wand and eclipse fluid. never use canned air and avoid 'blowing' the sensor as you have pretty moist breath and you also send tiny particles of saliva on the sensor which can smear.
jann - gently clean your mirror with a squeezy blower, soft bristle brush, or the corner of a soft lint-free cloth. the mirror can scratch pretty easily if you're rough.