How would astronomical seeing on Mars differ from that on Earth? Astronomical seeing is the limiting factor for the resolution of all but the smallest Earthbound telescopes. 

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Stunning advances in adaptive optics (along with it's predecessor speckle interferometry and it's budget-minded cousin lucky imaging) get around this but only with substantial compromises in (some combination of) throughput, cost, complexity and wavelength range (see answers to Why aren't ground-based observatories using adaptive optics for visible wavelengths?)

If identical telescopes sat on the surface of Earth and Mars and looked at a distant and equi-distant  body, how would the following differ between the Mars telescope and the Earth telescope?:
As far as I know, "seeing" (or rather the effects influencing optical wave propagation) is caused by turbulence in the atmosphere.

Using the Reynolds number Number $ Re = \dfrac{\rho L v}{\mu}$ as a measure for turbulence:


density $\rho$ drops due to the reduced pressure (about 1/100 earth pressure), additionally the gravity is smaller than on earth
characteristic length $L$ will stay similar
average wind speed $v$ is about 2 times higher than on earth
the dynamic viscosity $\mu$ of an (ideal) gas is independent on the pressure, and the temperature dependency can be approximated with $\sqrt{\dfrac{T_{mars}}{T_{earth}}} \approx 0.9$


So for an average martian day an atmospheric Reynolds number would be much smaller than on earth and I would expect a far better seeing due to less turbulence

Additonally, I would guess that the effects of a thinner and dryer atmosphere would help as well, since the index of refraction is dependent on the gas pressure as well.