Why does mounting an nfs share from linux require the use of a privileged port?

Why do you have to? Tradition, mostly. Once upon a time, restricting NFS to privileged ports (<1023) was considered a security measure. Back when people were using mainframe computers, this made sure that the NFS software on the client side was part of the OS/approved by the administrator, since a program can only use a privileged port if it's run by the root user. Today, this makes no sense because anyone can own a computer and have root access, so this doesn't mean anything in terms of security.

By default, many NFS servers don't allow non-privileged source ports. Some NFS clients (such as Ubuntu's), default to using a privileged source port unless otherwise specified, which is why your Linux client works without issue. Clearly, the OS X client doesn't do this. I don't know if that was an Apple design choice or something inherited from BSD. I know that Solaris also defaults to a non-privileged port.

The two ways of avoiding this problem are, telling the OS X client to use a privileged port, as you discovered, or configuring your NFS server to allow non-privileged ports (look it up in your server's documentation).

How do you get OS X to use a privileged port using a GUI? As far as I know, you can't on versions > 10.6. One used to be able to mount NFS shares in Disk Utility and type in extra options, but that was removed. (details) It was never a simple button or anything. NFS is hardly something most of the "non-techy" crowd need, so I guess it wasn't a priority and there are reasons routinely using privileged ports isn't a great idea.

I haven't tried it, but http://www.bresink.com/osx/NFSManager.html seems to allow configuration of OS X's NFS features without the command line.