Slitherine

The rules say that units must exit buildings "with as much as possible of their rear edge touching the building" but also that they "may leave in any direction".

What are the limitations of this? Can I exit anywhere in a 360 degree arc?

Or if the building is a perfect rectangle, do I have to leave at 90 degrees in any direction, or can I leave at 45 degrees - I.e out of one of the corners with my rear edge touching the corner?

You have to touch the sides. If you are touching a corner then you aren't using as much as your rear edge as possible.

But then I'm also unable to leave in any direction.

If I choose to leave at a 45 degree angle, then "as much as possible" of my rear edge is less than if I leave at 90 degrees, but still in line with the rule.

And let's face it, troops didn't only leave villages at 90 degree angles. If that's the rule, then maybe it's best to make all buildings round.

But then I'm also unable to leave in any direction.
If I choose to leave at a 45 degree angle, then "as much as possible" of my rear edge is less than if I leave at 90 degrees, but still in line with the rule.
And let's face it, troops didn't only leave villages at 90 degree angles. If that's the rule, then maybe it's best to make all buildings round.

Although not strictly the intent of the rule I suppose this is permitted. A 'building' could be a single large building or a number of smaller building, so no real reason why this shouldn't be allowed.