How to show multiple error messages simultaneously in form?

You can use separate variables for each type of error, and indicate them in the respective fields.

For messages to appear simultaneously, I've refactored your code, allowing each field to be treated separately:

<?php
   $page = 'Register';
   include 'header.php';

   $user_error='';
   $mail_error='';
   $pass_error='';

   if( isset( $_POST['register'] ) ) {
      $username = $_POST['username'];
      $password = $_POST['password'];
      $email = $_POST['email'];

      // Tratamento de erros do username:

      if( empty( $username ) ) {
         $user_error = 'Please insert an username';
      } elseif ( strlen( $username ) ) > 16
         $user_error = 'Username must have less than 17 characters';
      } else {
         // Essa linha abaixo é sujeita a SQL Injection, cuidado!
         $checkusername = mysql_query("SELECT 'id' FROM 'database'.'user' WHERE 'username' = '".$username."'");
         if(mysql_num_rows($checkusername) > 0) {
            $user_error = 'Username already exists';
         }
      }

      // Tratamento de erros da senha:

      if( empty( $password ) ) {
         $pass_error = 'Please insert a password';
      } elseif( strlen( $password ) < 8 ) {
         $pass_error = 'Password must have 8 or more characters';
      }

      // Tratamento de erros do email:

      if( empty( $email ) ) {
         $mail_error = 'Please insert an email';
      } else {
         // Essa linha abaixo é sujeita a SQL Injection, cuidado!
         $checkemail = mysql_query("SELECT 'id' FROM 'database'.'user' WHERE 'email' = '".$email."'");
         if( mysql_num_rows( $checkemail ) > 0 ){
            $mail_error = 'Email already exists';
         }
      }
   }

   // Se não setamos nenhum erro, e o formulário foi enviado, podemos ir para o insert:
   if empty( $user_error )
   && empty( $mail_error )
   && empty( $pass_error )
   && isset( $_POST['register'] ) ) {
      $insert = mysql_query("INSERT INTO 'database'.'user'('username','password','email') VALUES ('".$username."','".$password."','".$email."')") or die(mysql_error());
?>
<div id="sucesso">
   <h3>You are registered!</h3>
   <p>(aqui você pode por instruçoes, ou a mensagem que quiser, no caso do sucesso)</p>
</div>
<?php
   } else {
      // caso contrário, mostramos o form, e opcionalmente os erros encontrados:
      $user_error=empty($user_error)?'Username:' : '<b>'.htmlEntities($user_error).'</b>';
      $mail_error=empty($mail_error)?'Email:' : '<b>'.htmlEntities($email_error).'</b>';
      $pass_error=empty($pass_error)?'Password:' : '<b>'.htmlEntities($pass_error).'</b>';
      // O formulario está dentro deste else:
?>

<div id="loginform">
   <form name="loginform" method="post">
      <table cellpadding="0" id="tb">
         <tr>
            <td colspan="2"><div class="loginheader"><h2>Register</h2></div></td>
         </tr>
      </table>
      <table cellpadding="0" id="REGOPTIONS">
         <tr>
            <td class="field"><?php echo $user_error; ?></td>
            <td><input type="text" class="text" name="username"></td>
         </tr>
         <tr>
            <td class="field"><?php echo $pass_error; ?></td>
            <td><input type="password" class="text" name="password"></td>
         </tr>
         <tr>
            <td class="field"><?php echo $mail_error; ?></td>
            <td><input type="email" class="text" name="email"></td>
         </tr>
      </table>
      <table cellpadding="0">
         <tr>
            <td class="field"></td>
            <td><input type="submit" class="submitbutton" name="register" value="Register" /></td>
         </tr>
      </table>
   </form>
</div>

<?php
   } // Fechando o else acima

   include "footer.php";
?>

Thus, each error will be shown in its own field. This solution seems appropriate for your case, as there is only one error of each type being shown at the same time in your code (user, password and email).

If you want, the same% s of% s can be used and adapted to apply the @Otto solution, which is good if you want all errors presented in a single block.

<p><?php echo "'".$value."'<br>"; ?></p>

Switch to

$error =. "<p>".$value."<br></p>";

at the end of the loop echo $ error;