I had experienced similar problem after installing gallery and thematic themes.
After publishing any posts I got error which we are discussing here.

What I did and it worked for me is:

Change the “file_get_contents” with “curl_get_contents” in functions.php file from Appearances-Editor. Thats it. There was no file access error shows anymore in any posts!

I didn’t change anything which was mentioned in comment 12 and 13.

http://www.robinthomas.in/php/warning-file_get_contents-functionfile-get-contents-url-file-access-is-disabled-in-the-server-configuration/

Then discovered that, in working very late last night, I forgot that I had moved one of the key “require_once(‘xxx.php’)” files to another, more logical, folder on the server but had not updated the path to that file in the code of the related pages.

Thought this worth mentioning here because although the error message I was getting was the exact same message at the head of this thread but the actual problem was a moved file witout concurrent path updates, not a change in URL file-access per se.

$url = ‘http://www.example.com/file.cfm';
$request = new WP_Http;
$result = $request->request( $url );
echo $result['body'];

Some servers have allow_url_include disabled for better security. Starting with PHP 5.2.X allow_url_include is disabled by default. So you only two easy solutions are to:

1. Convince your web host to turn allow_url_fopen and allow_url_include on. Unlikely but they might do it.

2. Use CURL. papsy’s response #13 is really the easiest way to do this.