A PlayStation community team lead has revealed on the Official PlayStation forums how it is possible to play levels you’ve created which have been moderated.
Community Team Leader, MusterBuster states:
I have a solution for you!
Can I ask you to restart your console, and do not log in to the PlayStation Network.
Whilst offline, enter LittleBigPlanet and edit the level on My Moon - then save it on to a different slot.
Log back in, and re-publish
So there you go. Sony moderating levels and then Sony telling you how to get around it. Thank goodness there are dedicated community support staff around like MusterBuster to help out the more unfortunate of us. Top marks for Community Support MusterBuster!
If you’re still having problems with this, once your level is copied using the method above, you can save your level as an object and save to your library before placing it in a new level. If you have a very large level, you may need to save sections as objects, but both methods should work for re-publishing your content.
Naturally, we wouldn’t have to do this if levels were not being moderated in their rather heavy handed yet mysteriously uninformative way.