Different Variations of the Metropolitan Police Box?

[Volpone]

Again, just a pet theory of mine, but:
They went on to redesign and simplify the box for the Mark 5's
The door was wood--and thus prone to rotting (even teak can rot eventually)
From personal experience, wood rots most where the crossbars allow water to collect

I would make the case that IF there were widespread examples of boxes with the door hung backwards, it was a decision to try to reduce maintenance on the doors. 

Although that begs the question and just makes a guess. 

Whoops.  Misread.  Sounds like the Crich is the only extant example.  So I'm going to change my guess to "builder's mistake."