Games on Facebook.com can simplify their login with a parameter 'signed_request'. Learn how to modify your web flow to take advantage of this.
The features of Facebook Login make it safe and secure; there are security steps that your apps need have. Read this guide to for a simple checklist you should follow.
You may prefer to build their apps with both a custom login UI and Facebook Login. This guide will cover some of these scenarios and give you tips for handling someone's experience using these apps.
For particularly sensitive app operations like making purchases or changing settings, you may want to ask people re-enter their Facebook username and password.