Perhaps you could elaborate ?
It would be a real bonus to my theory that Madeleine left via the front door. So don't worry I would love to be able to prove the front door was open when Kate did her check.
"Gerry said the window was open, the shutters broken and the door, which had been locked, hanging open." that could be an attempt at saving face with his sister, "and the door, which had been locked, hanging open" you can't be sure which door he was meaning as in his first statement he came in via the front door.
The conversation with Jon Corner doesn't make logical sense either: "She just blurted out that Madeleine had been abducted. She told me, 'They have broken the shutter on the window and taken my little girl.'
"They had left the apartment locked while they were having their meal, but when they went back the last time they saw the damage.
"First they saw one of the window shutters had been forced, and then they saw the door was open and the bed was empty - and Madeleine was gone"
Kate would have seen the door before the shutters unless she was talking about the front door.
Putting in more detail if they came in through the patio door: "First they saw one of the [kid's bedroom] window shutters had been forced, and then they saw the [front door] door was open and the bed was empty - and Madeleine was gone"
Putting in more detail if they came in through the front door: "First they saw one of the [kid's bedroom] window shutters had been forced [from outside], and then they saw the [kids bedroom] door was open and the bed was empty - and Madeleine was gone"
I don't believe it is possible to be certain that the truth was being told in those first few explanations. I'd say it would be common for face saving to be done in circumstances like this.