After upgrading to 4.7.1, when trying to edit custom fields in tabs, the edit popup opens and you can enter data (and it does client-side validation) but the data is not saved.
Moving the set of custom fields to inline
rather than tab
is a successful workaround.
I couldn't reproduce it on demo, but I could on my dev site which has no extensions in common so I think it is unlikely to be due to an extension. I noticed demo is running 4.7.2 ... is this issue known to be fixed in 4.7.2? If so I'll just wait for the release and work around in the meantime.