I'm the admin who created a shared folder, but I'm getting a permission error when trying to edit a record.
Edit the shared folder and make sure to set the 'default folder permissions'. Click on the shared folder, then click 'Edit' -> then click on the settings icon. Set the 'Can Manage Records' and 'Can Edit Records' to give full record permissions on any record added in the future. If you have existing records in the folder, you need to individually grant the 'Edit' permissions on each record in the shared folder because 'default folder permissions' do not apply retroactively. If another user had created the existing records, that user must login and grant permission in the shared folder for each record.