Does the remote web site include CSS, JavaScript, or images?
If so, are any of the above resources referenced with relative links (i.e.: /javascript/script.js)?
If so, when the browser receives the HTML from your server, the relative links (which were originally relative to the source server) are now relative to your server.
You can fix this by either changing the HTML to use absolute links (i.e.: http://www.server.com/javascript/script.js). This is more complicated than it sounds: you'll need to catch <link href="..."/>, <a href="..."/>, <form action="..."/>, <script src="..."/>, <img src="..."/>, etc.
A more limited solution would be to place the actual resources onto your server in the same structure as they exist on the original server.