I was thinking of setting up my website with a file called master.php and using .htaccess and URL rewriting I would transform
http://mysite.com/About into http://mysite.com/master.php?selected=About
Which would allow me to setup the about page. Is it a bad idea to have one master page that creates dynamic pages?
No, this is fine. It is called a Front Controller pattern.
Just make sure you direct only page requests this way, and not requests for images, style sheets and other static resources.