Secondo me ci sono 2 errori

codice:
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<?php
//file dove memorizzare i dati
$datafile = "comments.txt";

$_POST   = isset($HTTP_POST_VARS) ?  $HTTP_POST_VARS : $_POST;
$_SERVER = isset($HTTP_SERVER_VARS) ?  $HTTP_SERVER_VARS : $_POST;

//verifico se il modulo è stato inviato
if(isset($_POST['submit'])){

    //
    $name = $_POST['name'];
        if($name == "")
            $nameError = 1;
        else
            $nameError = 0;

    $comments = $_POST['comments'];
        if($comments == "")
            $commentsError = 1;
        else
            $commentsError = 0;

    //se i campi "name" e "comments" non sono vuoti inserisco i dati
    //======= 1° Errore mancavano i graffi
    if($name != "" && $comments != "") {
     $new_content = "$name::$comments\n";
     $fp = fopen($datafile, "a");
     $fw = fwrite($fp, $new_content);
     $fc = fclose($fp);
    }
}

else {
    $nameError = 0;
    $name = "";
    $commentsError = 0;
    $comments = "";
}
?>
<html>
<head>
<title>PHP Comments...</title>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
<style>* {font: 10px verdana}</style>
</head>

<body>
<form name="modulo" method="post" action="<?=$_SERVER['PHP_SELF']?>">
Nome:

<input type="text" name="name" value="<?php echo($name)?>">
<?php
if($nameError)
    echo "<font color=red>Inserire il nome!</font>";
?>



Commenti:

<textarea name="comments"><?php echo($comments)?></textarea>
<?php
if($commentsError)
    echo "<font color=red>Inserire un commento!</font>";
?>



<input type="submit" name="submit" value="Invia">
</form>
<hr>

<?php
//verifico se il file esiste altrimenti lo creo
if(file_exists($datafile)) {
    $read_data = file($datafile);
    $num_comments = count($read_data);
    //========= 2° errore $c<$num_comments e non $c<$num_comments -1
    for($c=0; $c<$num_comments ; $c++) {
        $content = explode("::", $read_data[$c]);
        echo "Nome: $content[0]";
        echo "
";
        echo "Commento: $content[1]";
        echo "

";
    }
}
?>
</body>

</html>