With careful planning a reconstruction could have been informative.
A moving door was proposed as possibly showing that someone entered the apartment before Gerry's check. That possibility could have been checked out; was there time between Matthew's listening at shutters and Gerry's check. How did the person get in? Would they have heard Gerry coming and had time to hide? Were the available hiding places adequate?
Then we have the Tanner sighting. Was it possible for her to pass people and not be seen or heard? Was it possible for the shutters to be raised without alerting Gerry and Jez? Was it possible for others to pass the raised shutters and not notice? Was it possible for Matthew not to notice from inside the apartment? Was it possible to see children breathing from outside the doorway?
How were the patio doors left? Closed? Open a finger width? Open a hand's width? What was the minimum gap allowing them to be opened from outside? How exactly were they closed from the outside? Grasping the frame, pushing on the glass or what?]
What could be seen from the restaurant? Who sat where? What was the noise level like? What external sounds could be heard?