"During the climb, the flight crew noticed some minor Engine Pressure Ratio (EPR) fluctuations on No. 2 engine. No. 1 engine also had EPR fluctuations but within a narrower range."
Both engines had EPR fluctuations and therefore were not operating normally.
"At 0158 hr, when the aircraft was leveling off at Flight Level (FL) 390, the Electronic Centralised Aircraft Monitoring (ECAM) message “ENG 2 CTL SYS FAULT” was annunciated. As parameters on both engines were normal except the slight fluctuation of the EPR indications, both the flight crew and the MC were satisfied that it was safe for the flight to continue."
The EPR fluctuations continued on both engines and it appears the ECAM on engine 2 was discounted. Clearly at this point an outstanding job would have included a diversion to the nearest suitable airport.
"At 0316 hr, ECAM message “ENG 2 CTL SYS FAULT” reappeared. As all engines parameters remained normal except the EPR fluctuations, both the flight crew and the MC were satisfied that it was safe for the flight to continue to VHHH."
The EPR fluctuations continued on both engines and the ECAM on engine 2 was again discounted. Again at this point an outstanding job would have included a diversion to the nearest suitable airport.
"At 0519 hr, during the descent CPA 780 had the ECAM messages “ENG 1 CTL SYS FAULT” and “ENG 2 STALL” annunciated within a short period of time. At 0530 hr, ECAM message “ENG 1 STALL” was annunciated..."
There's nothing outstanding about ignoring problems that manifest themselves on both engines of a twin engine aircraft. There's nothing outstanding about the advice the crew received from Maintenance Control either - looks like commercial considerations were put ahead of flight safety. It is fortunate for the passengers and crew that this incident did not result in fatalities and a hull loss.