Hello,
JSON.parse runs synchronous and does not know anything about an err parameter as is often used in Node.js. Hence, you have very simple behavior: If JSON parsing is fine, JSON.parse returns an object; if not, it throws an exception that you can catch with try / catch, just like this:
webSocket.on('message', function (message) {
  var messageObject;
  try {
    messageObject = JSON.parse(message);
  } catch (e) {
    return console.error(e);
  }
  // At this point, messageObject contains your parsed message as an object.
}