WordPress wp-admin redirect and exception

The plugin update checker is outputting something before the login redirection. The function wp_redirect() has to be called before anything gets echoed onto the screen. Try disabling the anps_theme_plugin and see if your login problem resolves.

Edit:
I use a more complicated logging system that prints out nice and pretty on a custom admin page, but here is a temporary hack to the function wp_redirect() in pluggable.php This will stop execution immediately upon the error and tell you the last ten functions leading up to it. That backtrace will be an array.

The first and last lines are untouched, so you can see their location.

$x_redirect_by = apply_filters( 'x_redirect_by', $x_redirect_by, $status, $location );
    if ( is_string( $x_redirect_by ) ) {
        if (! headers_sent($filename, $linenum)){
            header( "X-Redirect-By: $x_redirect_by" );
        } else {
            $backtrace = debug_backtrace(FALSE, 10);
            echo '<br><br><br><pre>';
            print_r($backtrace);
            wp_die();
        }
    }
    if (! headers_sent($filename, $linenum)){
      header( "Location: $location", true, $status );
    } else {
        $backtrace = debug_backtrace(FALSE, 10);
        echo '<br><br><br><pre>';
        print_r($backtrace);
        wp_die();
        }

    return true;