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I'm a dispatcher at LGW and I know what you mean about cleaning up after passengers. Just today I dispatched 4 spins and I had an iPhone and an iPod handed to me by the crew. I've also had iPads kindles laptops. Briefcases unlocked with documents labeled strictly confidential. It does make me wonder how people leaves such things on aircraft.
With regards to security I have thankfully never seen GAL with their eyes on anything other than the screen they are meant to be looking at. Though dispite being in the EU all airports have different standards of security hence why international arrivals are kept away from departing passengers and domestic aren't. (according to a guy from DfT I was talking to) so I understand people getting touchy with electronics being left on-board. Especially after the mobile phone batteries scare we had.