I didn't see any security-related issues in this article. If you make your home computer "open to the public", you have to make sure "the public" won't be able to access your files.
First of all, you have to use strong passwords. Don't use the name of your pet or your dauther's birthday. Short passwords (3-4 characters) can also easely be compromised. You can add extra security to your password by using special characters in it (e.g. "&$*%)
Secondly, when you use AFP for transferring files over the internet, you have to be aware that the traffic is not encrypted. Any user with access to one of the public lines between you and your computer can read the files you are copying or using. Don't remotely access sensitive information, or use a file transfert protocol that encrypts everything. You could also use stunnel or ssh to encrypt the AFP session. Passswords, though, ARE encrypted with AFP. So you don't have to worry other people will gain access to your password.
Third, don't use protocols that don't encrypt your password. FTP is a good example. If you access your computer remotely just once with FTP, people between can know your password and all security is broken.
Those are just tree of the major security-related issues. I don't want to make you guys parano´d, but you have to be realistic these days. The governement is watching your traffic, too.