Thanks to mattlekim, who managed to get his not working world files out of his phone and emailed them to me, I now know what is causing the problem.
Any world that has pickable items present (i.e. stuff that drops off blocks when you harvest them) will not load. This is 100% my fault, as I forgot to include a subtle file format change in 1.4 -> 1.5 converter. Unfortunately all my test data did not have any pickable objects, so the bug slipped through.
The fix is very easy and I intend to submit it ASAP. Unfortunately that means you’ll have to wait another several days for it to pass the cert. But do not delete your worlds, they are perfectly fine. Just a small piece of data fails to load.
Again kudos to mattlekim! I fixed his world and will email him the fixed version, so he’ll be able to play immediately, if he can put it back on the phone.