you basically can't rely on transparency or shadows and effects from illustrator. they work most of the time, but if you want 100% problem free printing, the only way to go is to flatten stuff before you send it out.
for your pizza the square will be as a result of the edge of what i guess is either a .psd or .png file placed on top of your stripey bit.
you could just add a clipping path to the pizza as proper old school paths seem to still be problem free. but the easiest thing i find is as part of print readying stuff, select all text and vector objects, hide them, export the page or area as a tiff, delete that stuff, and re-place the page with the tiff, then un-hide your vector stuff showing back on top of the rasterized image. The end result is all the vector stuff stays super crisp, and al the transparency gets nuked so it can't cause you any issues. you can work with any files and images, dont worry about RGB CMKY transparency etc etc, as it all gets nuked into a single CMYK tiff, at the end in one go.
you can then check the images and transparency have been processed correctly by opening them in photoshop too.
when you save the pdf this time it will be problem free. its a bit of a work around, but it is guaranteed success.