I believe what you are seeing is called stitching. I'm not sure how to eliminate it, but searching for that term may help.
Do the white lines show in printing to a PostScript printer?
I think you are showing us a screen shot of a PDF from Acrobat Pro or Adobe Reader. The PDF is v1.3 where transparencies are falttened? What happens if you choose PDF/X-4 for exporting? Do the white lines still show up?
If you zoom in on the white lines do they grow in size? If not it's very likely a glitch in screen representation.
When in Acrobat pro or Reader go to "Preferences / Page Display : Rendering" and check/uncheck "Smooth line art". Do the white lines persist? If not it's only screen representation. Nothing to worry about.
There is an blog post about this phenomenon at InDesign Secrets (but it seems that the website is not available at times).
It's explained here:
Stop printing to postscript and distilling or using print to pdf.
Export the PDF to Acrobat 5 or higher compatibility.