There is one other thing that can cause fields not to save.
This could happen with nested repeater fields and flexible content fields on options pages and for taxonomy terms, it should not happen to custom fields for posts. It can happen if the generated option_name value is longer than 64 characters.
Is it repeater fields or flexible content fields on options pages or for terms? If so, what are the names of these fields and all of the nested fields?
If you imported the database, including any schema changes to the wp_options table then this should not be a problem, but it is something to check. What happens is that the option_name value will be truncated when saved then it cannot be retrieved later.
