How Do I Classify Dirty/Dusty Camera Images?
What kind of distortion does dirt/dust produce? If it is somewhat regular, for example more or less regularly sized speckles (greyish circles) it might be worthwhile to try to classify the logarithm of the real part of the fourier transform of the picture, instead of the original picture.

Also, knowing the physical properties of the distortion might guide you towards devising simple heuristics (for example based on some frequencies in the fuorier spectrum) that are as good as a ml-based approach.