These hairlines are due to flattening in the PDF.
Since the file is being flattened, I'll assume you are printing to a PDF/X-1a or PDF 1.3 (Acrobat 4) format. These formats are flat file formats. They don't hold transparency so when you export/print to these formats all the transparency effects must be flattened so the file will print correctly.
The hairlines are primarily an on-screen issue. You'll notice that when you zoom in and out, while viewing the PDF, the lines will move or vanish at one zoom level and reappear at a different zoom level, but they will never increase in size. These are anti-aliasing edges showing between blocks of raster images which were necessary for the PDF engine to create in order to maintain the file appearance in a flat format.
The hairlines should vanish when the PDF is printed.
If they really bother you, then you'll need to either flatten transparency before creating the PDF (why are you printing to PDF rather than merely saving?), or Save as PDF 1.4 (Acrobat 5) or PDF/x-4 so that the PDF format will support the transparency rather than flattening it.