1. With the lasso tool, select the area you want to clean up. Under the Layer menu, select New > Layer Via Copy (or just hit Ctrl+J on the keyboard)
2. With your new layer active (A), select the Move Tool (B)
3. Using the arrows on your keyboard, nudge the layer out of place. I usually start by going down 4 pixels and then to the right 4 pixels. Experiment with how much and in what direction works best for the image you're working on.
4. Reset blending mode. If the dust/damage is darker than the surrounding area, choose the Lighten mode. If it is lighter, choose darken.
5. I also sometimes add a slight Gaussian blur to the new layer before flattening.
This method of cleaning an area works well with most large, fairly even areas (such as sky).