SCCM 2012 R2 - Content never appears on Distribution Point, stuck 'In Progress'

Problem

You try deploying an application to a remote distribution point, but nothing seems to show up. The little pie chart of progress refuses to turn green for the DP you're trying to deploy to:

Furthermore, checking the Content Status shows that the DP is waiting for you to pre stage the content.

Cause:

Somewhere there's been a mix up between how you think content should be distibuted (i.e. automatically) and how the new DP thinks it should be getting content (i.e. manually).

Fix:

You need to change the distribution point settins or the applicaiton deployment settings...or you might even need to change both.

The DP

If the Distribution Point has been set to be "Enabled for prestaged content" then it will be expecting content to be manually copied to it. Untick this box to remove it's presumption that all content will be prestaged:

The Package

If the package has had its 'Prestaged distribution point settings' set to manually copy the content to the dp, then the dp will, quite reasonably, be expecting you to manually copy the content onto the dp. Open the properties of the package and make the change under the Distribution Setting tab:

Try re-distributing the package with the new settings in place and you should find it now automatically deploys to the DP.