I was on a LH flight not long ago, maybe last year. European short haul, I think it was an Embraer. They taxied and lined up with the cockpit door open. To my surprise they then started the takeoff also with the door open. A CC member then only got up to shut the door a few minutes into the climb. I did find it a bit strange that such an obvious thing could go unnoticed by so many different crew members (2+2). Made me wonder about the level of attention going on in that cockpit.