Illustrator vector images imported into Indesign look bad in PDF
I'm using Indesign with intent to print, and I placed some of my Illustrator image-traced pictures onto the pages, and they all look fine in the Indesign workspace. Once exported to PDF/X-1a:2001 in acrobat 4 I see a ton of white lines showing up randomly in my images. Some I can tell are remnants from where I used the pen tool and made a shape in Illustrator, and some are just random white lines that appear for seemingly no reason. Is there any setting/quick way to fix this in Indesign without having to go back into Illustrator and re-editing all my images? I added an image to show what it looks like. 
