What is the range of possible atmospheric pressures on the surface of the Earth?
Presssure at the Mt. Everest summit has been measured to be 253 Torr (337 hPa).  http://jap.physiology.org/content/86/3/1062

Pressure at the Dead Sea as high as 1079 hPa is reported in Fig. 12 of this reference: http://isramar.ocean.org.il/isramar2009/DeadSea/Hecht&amp;Gertman_2003_DS_Climate_Chapter4.pdf 

As far as at sea level, 870 hPa was measured for typhoon Tip in 1979. http://www.wunderground.com/blog/weatherhistorian/world-and-us-lowest-barometric-pressure-records

And 1067 hPa at coastal areas of Estonia and Lativa are reported here: http://www.wunderground.com/blog/weatherhistorian/world-and-us-anticyclonic-high-barometric-pressure-records