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On earth we have launch windows because of this and constant weather monitoring is needed right up until launch. Would this be required on a return trip from Mars given that the speed of the wind on Mars combined with the atmospheric pressure make the winds feel very weak.

Plus there are dust storms to consider. Would those affect the launch?

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This related to, but not a duplicate of Are Martian winds as strong as portrayed in "The Martian"? Answers there show that because the pressure is so low on Mars, even a high wind velocity doesn't result in that much force. You would feel a windstorm on mars, but it wouldn't be enough to knock you down or blow a rocket over. So, from a wind perspective it's unlikely a launch window would be delayed.

Dust on the other hand may be a bit more of a problem. Dust storms on Mars can get pretty high, up to 40 mi/60km in the atmosphere. At ground level the dust isn't likely to be that much of a problem, at 20km up a launch vehicle would be going at a very high rate of speed, so dust particles could damage the leading surface.

However dust isn't likely to stop a launch. Mars dust storms can last for weeks, even months, so designers would have to build a solution into any spacecraft that would need to return to orbit or meet a launch window back to Earth.

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