According to the Wikipedia page about MJPEG (http://en.wikipedia.org/wiki/Motion_JPEG#M-JPEG_over_HTTP), the MJPEG stream over HTTP is basically a sequence of JPEG frames, accompanied by a special mime-type. In order to capture these and save them to a video file, I am not sure you can simply write the incoming data to an .mpg file and have a working video.
To be honest, I am not quite sure why your script does not write anything at all, but I came across the following page, which, although it is written for specific software, provides examples on how to capture an MJPEG stream and pass it on to a browser:
http://www.lavrsen.dk/foswiki/bin/view/Motion/MjpegFrameGrabPHP
You could try one of their examples, and instead of passing it to the browser, save it to a file. You can see they read one image at a time:
while (substr_count($r,"Content-Length") != 2) $r.=fread($input,512);
$start = strpos($r,'ΓΏ');
$end = strpos($r,$boundary,$start)-1;
$frame = substr("$r",$start,$end - $start);
If this does fix the stream capturing part but not saving it as a video, another option would be to save all frames individually as a JPEG file, then later stitch them together using a tool such as ffmpeg to create a video: Image sequence to video quality
Update
If you decide to take the ffmpeg road, it is also possible to capture the stream using ffmpeg only. See this question for an example.
Hope this helps.