I just recently run into a problem using shared distribution points, some applications would just not download anymore.
After some troubleshooting I found out that the application had different Content ID when I compared the source- and target application.
Then I found this great aticle to explain the issue:
https://blogs.technet.microsoft.com/configurationmgr/2015/09/30/configmgr-2012-support-tip-migrating-an-application-to-a-new-hierarchy-creates-new-content-id/
