The easiest way is to clean your lens before shooting and make sure your sensor is also clean.
I had a "smudge" on my lens that I was not aware of until looking at a blue sky. Then it became apparent. I now double check to make sure the lens is clean on both ends, along with the sensor. A few seconds of my time.
Just wondering how something as complex as removing dust from lens/sensor would be. How much would it cost to create this feature. After Effects has it, and so does BorisFX.
This works with still images. I don't see why it shouldn't work with movie clips.
Take a still image shot which is out of focus against a plain background such as a blue sky or white sheet of paper but make sure the lighting is even. That will ensure only dust spots are picked out as they are against the sensor.
Place the image into a photo editor that can create a PNG file.
Find your dust spots. Carefully erase around the dust areas and save with a transparent background. Turn the black spot into a white spot.
Save and exit.
Place the image on the lowest track of the project. Add lots of blur.
With the Chroma key tool pick a blending mode that makes the dust spot blend best.
If you have big or many dust spots forget it. Clean your sensor.
You may have to change the blending mode from scene to scene but that takes less time than to render with something like Neat Video.