They did not take off with a "partially open door". The article you posted clearly states that the malfunction arose during flight after the aircraft had already entered Pakistani air space. After which the crew decided to land at the nearest available runway. On top of that, we don't exactly have any idea what the malfunction actually was. No where does it say that the door was open, even if partially. Chances are that it was something very minor.
Believe it or not, malfunctions do happen with aircraft all the time, all over the world. I've seen an Etihad flight's engine blow up and catch fire a few hundred meters above my head right after take off.
I'm not trying to defend the PIA, it is a third rate airline destroyed by the third rate service and professionalism of its crews in the air and on the ground. That said, this needless ruckus we create every time just to satiate our appetite for "mirch masala" needs to stop.