Hi Archbob - Welcome to PSG. FWIW, the slightly darker, very soft-edged areas in the upper RHC of your image look more like dried / smeared water or oil spots on the sensor, not dust. At f/11, the aperture at which you took this picture, dust on the sensor would show much, much sharper edges, more structure, and the majority of dust particles usually are much smaller than what you have.
The reason for making this distinction is because if the problem only involved a few pixels, the automated methods of dust spot removal usually work quite well. However when problems occupy this much real estate in the image, I'm afraid you are probably stuck removing them manually. The distinction is also important in terms of how to remove them from the sensor -- specifically, if they indeed are dried water spots, you won't be able to just blow them off.
The more recent versions of LR (v5, and after, I think) do have a very nice automated tool to remove dust and other spots that remain in the same position from frame to frame. Here are two links to articles about this tool:
http://digital-photography-school.com/how-to-remove-dust-spots-from-multiple-photos-in-4-steps/
http://photographyessentials.net/lightroom-auto-spot-removal/
Unfortunately, while this tool does have some intelligence built in, it is not magic, and when spots this size occur in areas with important features / texture, you probably won't be happy with its result. When problems occur in important / textured areas, you are better off learning how to fix the area manually using either:
1) The patch tool - for relatively easy to fix problems with irregularly shaped boundaries.
2) The content aware fill tool - for more difficult problems (also with irregular boundaries)
3) The spot healing brush tool - in either conventional or content aware mode ... best with simple / small circular areas.
4) The clone tool.
My guess is that Sam recommended #4 because of the old version of PS that you own. However, if you are serious about working on this problem and your time is valuable, I would (at minimum) rent the newest version of PS for a month or two (at a very reasonable cost) because it includes all the new tools, as well as includes refinements to older tools.
The difficult in using the above tools ranges from trivial, very easy to use -- almost one click fixes, all the way to being quite difficult and requiring lots of experience. It all depends on what the spot is covering, how big it is, and if you can find other areas of the image that you can steal pixels from. Fixing the spots in the sky in image you posted is trivial - I simply used #3 in content aware mode. It took me under 1 minute to get rid of these spots. Other images can be much, much harder.
So, if you have lots of images of the latter type, prepare to Google tutorials on the use of these tools and develop your skills by practicing.
HTH,
Tom M
PS - Because this thread is about water marks, not dust, I'm going to change the title of the thread for anyone looking for info on this topic in the future.