It’s a common problem – digital sensors attract dust and each time you swap lenses you run the risk of a bit of dust entering the camera body and ending up on the sensor. Dust shows up as small grey fuzzy disks which appear ‘sharper’ if the image was taken at small apertures as opposed to wide ones (more Depth of Focus, which is like Depth of Field but operates behind the lens).
Fortunately, Lightroom 5 has a handy tool to allow you to ‘spot’ the more subtle dust blemishes.
In the Develop Module, select the Spot Removal Tool (Q key). Now look down at the bottom left of the image and you’ll see a Visualise Spots checkbox and slider. Click the box, and adjust the slider until the dust appears clearly against a black background. Dust usually shows up as a white doughnut, white specks like stars will look like solid spots and can be avoided.
Click the spots using a brush just slightly bigger than the spot (mouse wheel or square bracket keys to re-size) and use the Heal setting for best results. You should now see a brush ring marked on the image – if not toggle this on and off with the H key. You can even drag the sampling source ring around to choose a better place than the automatic selection provides.
Lastly, given that dust on the sensor will be on the same place in many images, you can multi-select images and ‘Sync…’ the Spot Removal settings from one image to many. A huge time saver.