It's still there in the 1988 regulations:
120 Weather reports not to be used if not made with authority
(1) The operator or pilot in command of an aircraft must not use weather reports of actual or forecasted meteorological conditions in the planning, conduct and control of a flight if the meteorological observations, forecasts or reports were not made with the authority of:
(a) the Director of Meteorology; or
(b) a person approved for the purpose by CASA.
Penalty: 5 penalty units.
(2) An offence against subregulation (1) is an offence of strict liability.
Note: For strict liability, see section 6.1 of the Criminal Code.
But note: The 1988 regulations are being rewritten, so the above will be gone and replaced by around the year 2000.
AIP GEN 3.5 para 4.4.2 says: "For the purpose of aircraft weather reporting and observing visibility for takeoff and landing at an aerodrome, the pilot in command shall be deemed an approved observer for that flight." Given the use of the very impressive words "shall" and "deemed", that seems to be an approval under CAR 120 for PICs in the limited purposes stated.
Dunno if UNICOMS get an approval.
I never look at those aerodrome webcams to see what the weather and WDI are doing. My understanding is that they shall have been deemed not to be approved. Hopefully they will be, by around the year 2000.