I created a file with all the text boxes and images in the exact same position on every page. However when I export it as a pdf, the elements especially the images move out of position like a couple of pixels. Is this a flaw in MS Word and there's no way to fix it? I'm using MS Office 2007.

Word is a word processor, not a graphics program or even a professional page layout program. While I have never experienced it, it does not surprise me that objects could move by a couple of pixels. I would not call that a flaw for a word processor. For me a pixel is about 1/87ths of an inch.
You might try placing the objects in table cells.