There are a few reasons why the door could have been left in a 45° position. What is important is that the door had reportedly been moved & without knowing who moved it or why, any attempt at analysing its exact position when Kate arrived at 5A is http://miscarriageofjustice.co/Smileys/custom/c029.gifpointless imo.
The different positions of the bedroom door between nine and ten was of great importance at the time. It would only have been noted once statements had been taken and the information collated. In my opinion the earliest that could have happened would have been after the interviews on the 4th May.
Working on Kate's description of the bedroom window and shutters, Matt's description of light coming from the area of the window and outside in combination with the door movement I think there was a line of inquiry there begging to be followed through.
Particularly when Jane's sighting of the man carrying a child is added to the mix.
The whole investigation into Madeleine's disappearance might well have followed a different direction lasting days.
Instead we had the first leaks to the press with the publication in Diario de Noticias: "Headline: a badly told story." an illustration of how badly off tangent the investigation was taken by ignoring the testimony of the witnesses.
It was all downhill from there.