doubleu-anker, that incident you're referring to isn't quite accurate. First off, there was an disagreement between both pilots which resulted in the co-pilot being relieved of his duties (later suspended). Secondly, a relief pilot was brought in to fly the domestic sector. Thirdly, this did not occur on an EgyptAir flight but on another airline who have since gone bankrupt.
As for the EgyptAir/EU issue, the airline took immediate remedial action when it was informed of the findings. I understand the recent management reshuffle (new CEOs & VPs for the holding company and airline) was in part instigated as a result of safety shortcomings revealed. Without a doubt this was an embarrassment for the airline, since they've made great strides in improving their operations, product and image over the past few years. Hopefully this will instill a stronger safety culture within. I believe the airline has the potential to be leading carrier in its market.