I agree, tangentially, with the previous posters that the biggest single engineering controversy in current commercial aircraft is cockpit controls philosophy.
(There are other big issues, but they relate to human factors: crew fatigue, training, automation dependency, etc.)
For the most part, engines, airframes, deicing, etc. are more or less "sorted" - they work as designed, and where there are issues, they are generally manufacturing QC or maintenance problems, not basic design problems.
If your brief is producing a bolt-by-bolt critique of one single aircraft design, that's something else yet again. But clearly Airbus' unique selling proposition (and according to many, its Achilles Heel) is the fly-by-computer philosophy, and how it is implemented by Airbus, in the pilot-aircraft interface.