hook_link_alter() expects $comment as a third argument.

hook_link_alter() in D6 can be used for nodes and for comments.
hook_link_alter(&$links, $node, $comment = NULL)

Have a look at comment.module, function comment_render() in D6
(I don't want to give line numbers, they could change with the Drupal build).

<?php
        $links = module_invoke_all('link', 'comment', $comment, 1);
        drupal_alter('link', $links, $node, $comment);
?>

And now in advanced_forum.module, function advanced_forum_preprocess_comment()

<?php
      $links = module_invoke_all('link', 'comment', $variables['comment']);
      drupal_alter('link', $links, $node);
?>

Correct would be

<?php
      $links = module_invoke_all('link', 'comment', $variables['comment']);
      drupal_alter('link', $links, $node, $variables['comment']);
?>

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Why is this relevant?

Because in my implementation of hook_link_alter(), I want to check whether I'm dealing with a comment or a node.
I need hook_link_alter(), because it is the only comment hook that has $node as a parameter in addition to $comment, so I can check for $node->type.