Many books and articles suggest this method as a safe alternative when lacking water filtration or purification methods. Without testing equipment some methods are difficult to prove. Norseman of Survivology 101 posted two great blogs which include testing done while he trained with the Norwegian school of Winter Warfare. The testing shows that the Mash or Seep showed zero improvement in lowering the bacterial count. Norseman is a retired Marine who held a Scout Sniper Survival instructor position at the First Marine Division, and SERE instructor.
Advantage is that you are not adding any chemicals to your water, which takes out the guess work as far as dosage. The disadvantage, if it can even be called that, is that you have to have a source of heat(fire, stove, etc.) in order to bring the water to the boiling point. Also we have to remember that this does not remove chemical such as petroleum or pesticides which can be harmful as well.
STAT: The number of annual deaths from ESD in the U.S. are unknown, since they are counted among all drownings. But anecdotal evidence shows that ESD is widespread. ESD prevention groups have successfully urged some states to enact safety standards, including the installation of ground-fault circuit interrupters and a central shutoff for a dock's electrical system.