Hi Tobias!
I had the same issue importing HTML files described by @va_swimmer.
I have just made the fix you proposed and it worked.
Please try changing line 178 of the classes/class-import.php file from
$table = simplexml_import_dom( $dom_tables[0] );
to
$table = simplexml_import_dom( $dom_tables->item( 0 ) );
Thanks for your help!
Adrian.