I'm using the Import Multi-value Custom Data screen (civicrm/import/custom?_qf_MapField_display=true) and it does work, but it is not saving the field mapping. There is the following error:
Warning: Declaration of CRM_Custom_Import_Parser::run($fileName, $separator, &$mapper, $skipColumnHeader = false, $mode = self::MODE_PREVIEW, $contactType = self::CONTACT_INDIVIDUAL, $onDuplicate = self::DUPLICATE_SKIP) should be compatible with CRM_Contact_Import_Parser::run($tableName, $mapper = Array, $mode = self::MODE_PREVIEW, $contactType = self::CONTACT_INDIVIDUAL, $primaryKeyName = '_id', $statusFieldName = '_status', $onDuplicate = self::DUPLICATE_SKIP, $statusID = NULL, $totalRowCount = NULL, $doGeocodeAddress = false, $timeout = CRM_Contact_Import_Parser::DEFAULT_TIMEOUT, $contactSubType = NULL, $dedupeRuleGroupID = NULL) in require_once() (line 17 of /srv/buildkit/build/dmaster/web/sites/all/modules/civicrm/CRM/Custom/Import/Parser.php).
There are also additional errors for each field used in the import:
Warning: Invalid argument supplied for foreach() in CRM_Custom_Import_Parser_Api->import() (line 180 of /srv/buildkit/build/dmaster/web/sites/all/modules/civicrm/CRM/Custom/Import/Parser/Api.php).
I reproduced this error on the dmaster demo site and am using the errors from this site.