Are there any Airworthiness Directives for the Boeing 777 that might explain MH370's disappearance?
Are there currently any ADs for Boing 777s which would indicate the potential for catastrophic electronic system failures that might explain MH370's transponder failure and other issues?


No one of the ADs issued for 777s can by itself fully explain all the facts of the final flight of MH370/MAS370. 

Basic facts


The aircraft was a 777-2H6ER with 53460 flight-hours and 7525 take-offs and landings
A 777 has three VHF radios, two HF radios and two transponders.
Modern airliners have two main generators, an auxiliary power unit(APU) and a ram-air turbine(RAT) for emergency power. I think the 777 also has backup generators and two independent main power buses.
The aircraft left Kuala Lumpur for Beijing on 8 March 2014 at 00:14 local time with 239 passengers and crew on board.
Communications were normal up to and including 01:19 when someone on board (believed to be the co-pilot) said to ATC KL "Good night, Malaysian three seven zero". This was the point at which ATC control is handed to Vietnamese ATC. After there were no further communications from the transponder, the ACARS system or from the VHF radios.
Malaysian military reported that their primary radar system records do contain information on an unidentified aircraft to the northwest of Malaysia. The timing, position and heading of the unidentified aircraft in this report are consistent with MH370 changing course away from its intended flight path.
MH370 did not arrive at Beijing at 06:30 as scheduled.
A satellite communications system on the aircraft continued to respond  to routine hourly handshakes from an Inmarsat ground station via satellite 3-F1 located at 0.0°N (±1.59°), 64.5°E at a height of 35786 km. These normal handshakes ceased after 08:11, there was an unexplained incomplete handshake at 08:19.
Subsequent analysis of the handshakes is consistent with MH370 continuing into the southern Indian ocean (and somewhat inconsistent with other routes or it being stationary)
Countries within range of the plane's potential flight paths were asked to check their primary radar records for signs of MH370. No country reported finding anything.
No part of the aircraft or its contents have been located and firmly identified.
Many months later, some parts from the aircraft were washed ashore. 
Investigators report that the condition, timing and location are consistent
with ocean currents from a point in the south Indian ocean.


Electrical failure hypothesis

Anyone speculating about the fate of MH370 needs to fit their hypothesis to the above facts.

They would have to explain how the failure incapacitated multiple systems within a few minutes and before any of them could be used.

In particular what did NOT happen:


The pilots did not make an emergency broadcast on VHF
The transponder did not squawk any emergency code
The ACARS system did not continue normal communication
The aircraft did not return to KL and follow procedures for loss of communication.
The aircraft did not continue on its planned route
The aircraft did not arrive at any of the airfields a pilot should divert to in emergency.


And what DID happen


The aircraft remained airborne for a further 7 hours.


Therefore the engines continued to run

Electricity was available to a satellite communications system on the aircraft.
The aircraft most likely deviated from its planned route.


AD 2014-05-03

This AD issued Feb 18th was reported on in March in connection with MH370.

But Reuters reports that Boeing stated this AD does not apply to the aircraft used for flight MH370. 

If you ignore that and look at the consequences of a fuselage crack in the vicinity of the satellite antenna, you can see that this would not turn off the transponder, would not affect the VHF aerials and, if it caused a slow decompression - does not by itself explain why the crew would have failed to respond to the resulting low-pressure alerts by donning oxygen-masks, contacting ATC and descending to a safe altitude.



Occams razor

A shortage of facts always leads to speculation. Some of which can be very imaginative. The onus of proof is on those producing the hypothesis.

I'm sure there are thousands of hypotheses but, in my opinion, the simplest explanation I've read which is consistent with the known facts is deliberate action by a pilot or persons unknown. This doesn't mean it is the right explanation, just that it seems the most probable to me at the moment.




  Was the aircraft used for MH370 in compliance with all ADs?


We won't know with any certainty until the investigations branch of the relevant regulatory authority publishes their report on the incident. In previous accidents over an ocean, it has, on at least one occasion, taken years before a final report could be written.

Currently, there have been no confirmed reports, that I can find, of an AD that warned of the potential for catastrophic failures and which should have been applied to 9M-MRO and wasn't.