Exported PDF from Illustrator prints with extra lines not in original file

I can't tell from the previous images that were posted, but are you seeing the extra lines when previewing the PDF on screen in Adobe Acrobat or Adobe Reader? Or is the glitch something that is only appearing on printed pages? If the error is only happening in print then I would wonder what kind of printer was being used and its capabilities of processing PDF-based content.

We have an office laser printer at my workplace that does a lot of general purpose document printing. Even though this printer is bigger than a washing machine it stinks at printing Illustrator AI or PDF files. If the artwork has various kinds of clipping effects or transparency effects it's prone to delivering yucky discolored box syndrome on printed sketches. Our large format RIP applications have Adobe certified PDF print engines. When the same PDF files are processed by those apps the artwork prints perfectly.

Here is the file. 

I've saved it as an Acrobat 7 PDF 1.6 

How are you saving the PDF? Press Quality? Are you using a lot of transparency in the file?

If so the PDF needs to be at least version 1.4

What is the color space of the document RGB? CMYK? Make sure you're not mixing color spaces, especially if using transparency in the document.

I wonder if you have image files in your PDF?  Are the lines random or in the same place every time you print?  Take a look at your original Illustrator file.  Did you update any image links?  Check the file in outline ( command-Y ) mode and see if hidden elements show up?  Really hard to pin it down without seeing the files and/or prints.