Omega's override of theme_field() allows attributes to be set for each field item, as a preprocessor function can set $variables['item_attributes'][$delta]:

    $classes = 'field__item ' . ($delta % 2 ? 'odd' : 'even');
    $output .= '<div class="' . $classes . '"' . $variables['item_attributes'][$delta] . '>' . drupal_render($item) . '</div>';

However, the CSS class can't be set, as that is hardcoded and only has field__item and the odd/even class. It would be useful to also have $variables['item_classes'][$delta].

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joachim created an issue.