It's a few years since I researched these matters so please go steady if I'm out of date!
I believe in the UK that the published aerodrome elevation is the "highest point on the landing area" whereas in many States (ICAO definition?) the published aerodrome elevation is that of the Aerodrome Reference Point which is normally around the "middle" of the airport or main runway.
As has been stated previously the pressure is normally measured to one tenth of a Hpa but if ATC are passing a pressure setting it is corrected down to the nearest whole Hpa. E.g Pressure =1010.9 Hpa would be passed as 1010 Hpa - this would account for .9 X 27.3 = 25 feet as an "error" but on the "safe" side.