It's possible that your document contains images or objects that are partially transparent, which we call transparencies. These transparencies are usually not visible in your file, but can not be handled correctly by the printer.

This looks as follows:

Faulty flattening

Good flattening

Therefore it is important that you remove any transparencies by flattening your files. Here's how to do this: In Illustrator you can flatten transparancies directly by using the "Smoothness transparency" option under "Object". In InDesign, do this as follows: Create a new profile under the 'Edit' tab. Choose what kind of resolution you want (high resolution), click on "new" and name your file. Then set the 'Grid / vector balance' from 100% to 75%. Then check the bottom box "Compressing Complex Regions". The other options are fine, so now you can confirm the settings by clicking OK. Then export your design to PDF and choose from the PDF menu at the top of the PDF / X-1a: 2001 preset. Choose from the "Advanced" menu on the left side "Transparency smoothing" for the newly created 'smoother' .