This is caused by transparency. This FAQ will not go into the technical details behind transparency (Adobe’s technical documentation on transparency is over 100 pages long).
Simply put, applications tend to split up a page in small square areas called atomic zones. The effect of transparency is then calculated for each separate atomic zone. The stitch between atomic zones can sometimes show up on-screen as thin white lines.
To simplify things, be sure that your final PDF does not contain transparency. Using the Preflight features of Adobe Acrobat Professional, you can diagnose the issue by listing any transparent objects.
You can then use the Flattener Preview tool to create flattener presets, which can be loaded into the PDF Optimizer tool to output a non-transparent PDF file.
In InDesign, check the pages list for pages that have a checkerboard pattern – these pages contain transparent objects, which should be flattened before export.