one way to parse this is to assume all the "dust" on the mirror represents a surface area within the light column defined by the aperture. say the mirror is filthy, and this amounts to an area that is 10% of the aperture area. this amounts to 30% of the aperture diameter.
if the scattering is at the supramicron diameters (mie scattering) of most surface dust particles, then they are essentially reflecting the light, so everything depends on the reflectance index of dust. equivalently, the amount of light reaching the image plane from this dust will be equal to the amount of light reflected from a disk of pure dust that is 30% of your aperture diameter. say the reflectance is a neutral gray, the reflectance is 20%. surfaces scatter light randomly, so only the light that reaches the secondary mirror will be reflected to the image, so this depends on the angular width of the secondary as observed from the mirror distance. say this is an ƒ/8 newtonian with a 25% obstruction, then the secondary will be 0.25/8 radians wide or ~3º in angular area, which is 1/6240 of the forward half space area of about 20,000º into which light will be scattered. some of this scattered light will be reflected outside the area of the field stop, a further reduction i ignore, so the net forward scatter will be 20%/6240 or 1/31,000th the light falling on the equivalent mirror area.
if you assume submicron or rayleigh scattering, where photons interact with material atoms or molecules, then you might replace the 20% reflectance of dust with the 60% reflectance of a sky blue lambert disk, which means that you have no more than 1/10,000th of the light reflected into the image.
this analysis suggests why many experienced and grizzly astronomers are far more interested to port their telescopes to dark sky sites than to emblazon their objectives or corrector plates with sleeks by cleaning off a bit of dust.
it also supports glenn's contention, since we are talking about contrast and no more than a 1:10,000 difference in illuminance. i think that will have a very small leverage to brighten the dark areas of a low contrast target such as jupiter's whorls. small exit pupils acting as pinholes can project dust or motes into the image.
in general the problem of scattering arises from material surfaces parallel with the optical axis and from insufficient surface polish in eyepiece lenses or objectives. to the extent refractors have an advantage then i think it comes from the lack of central obstruction, tube baffling, and the antireflection coatings on the objective, which i beleive act as a very weak light pollution filter.