Possibly since the last versions of 4.6 but certainly in 4.7 we're unable to select any profiles for the online registration screen for events. Even for a new event we get the "The selected profile is using a custom field which is not assigned to the "Event" being configured" warning, and we can see only two profiles (Discount Codes and End Dates) - we get this warning even though at this stage we haven't picked any profile.
This is Joomla 3.4.8 and Civi 4.7.1. It's a default Joomla template and I've removed all Civi extensions for the moment. I'm accessing as a SuperUser so it isn't a permissions thing.
Unfortunately the demo server is running Civi 4.6 so I can't try to replicate the issue there.
Any suggestions where I should look?