Apologies again for the issue. After doing lots of digging, I have been able to reproduce and diagnose the problem, which is a bug on our side. Unfortunately this fix will not show up until our next release (early December), but a work around is available.
Workaround:
1. Open the web map used in the Shortlist app in the ArcGIS online web map viewer.
2. Click 'Share' button, then 'Create a web App' button.
3. Pick the Shortlist app.
4. The Shortlist will then launch in a mode that will allow you to use your existing Shortlist point layer as the data source. The app will copy the web map to a new web map, preserving all of the work you did in adding places and all of its information. You should then be able to continue adding places successfully.
We hope this is a reasonable solution to your problem and does not eat up anymore of your time. Let us know if you have any issues with this work around and we will do our best to get you back on track.
-Mark