Radar mosaics are composite images from several radars. The simpleminded approach for creating a mosaic works pretty well: for every location in the mosaic, plot the highest value of reflectivity observed by any radar. More sophisticated mosaic constructions might blend the data from two or more radars together to avoid sudden jumps where one radar gets out of range.
Mosaics are tremendous for allowing the forecaster to see the big picture and to understand how the whole storm system is developing. However, the forecaster must always be mindful that the composite is just a combination of several individual radar images, with all the limitations associated with a single radar image.
For example, take this radar mosaic from the Central United States.
Apparently, it's a straightforward image, showing lots of snow showers, particularly along the Appalachian Mountains. But notice how the radar echoes seem to lie in clusters: there's one cluster in central West Virgina, another cluster in southwestern Pennsylvania, another cluster in northeastern Ohio, another cluster in central Pennsylvania, and so forth. This clustering effect is caused by the shallow nature of these particular snow showers. At about 100-150 km from the radar, even the lowest radar beam is higher than the precipitation echo, and so the snow showers only show up close to the radars. Looking at this mosaic, you can pretty well infer the locations of the radars: Charlestown, Pittsburgh, Cleveland, State College, and so forth.
A good forecaster, looking at this image, would know that the true distribution of precipitation is much more continuous, and probably forms a solid swath of showers from Kentucky to northern Pennsylvania, without the breaks that show up on the radar mosaic.
Also, because of the distance/elevation effect, the spacing of the radars, and the blocking effect of mountains, many parts of the United States, particularly out West, are not covered by any radars at all. Thus, on a radar mosaic, it will look like it never rains or snows there. The best way to identify such areas on the fly is to look at an animation of radar mosaics: you will see echo apparently appearing as it enters the range of a radar, and apparently disappearing as it leaves the range of a radar. By combining a sequence of radar images with satellite and surface data, you can infer a complete picture of the precipitation distribution.