How can I redirect user after entering wrong password?

I’m using wp_login_form() to display login form in a jQuery dialog window.

If user enters wrong password, the user is taken to the backend. I don’t want that. Is there a way to notify user that he entered wrong password and still remain on the same page?

Before wp_login_form() came I was using a plugin. I’m kind of hoping I can avoid using a plugin for this.

My code:

wp_login_form( array(
  'label_remember' => __( 'Remember me' ),
  'label_log_in' => __( 'Login' )
) );

wp_login_form() creates a form with an action attribute of site_url/wp-login.php, which means that when you click the submit button the form is posted to site_url/wp-login.php which ignores redirect_to on errors (like wrong password) so in your case either go back to using a plugin or recreate the whole login process and that way you will have control on errors, take a look at Check for correct username on custom login form which is very similar question.