Make sure that every path gets a thin stroke in the same color as the fill.
I wouldn't know how to do this automatically in Inkscape or AI, but depending on your how geek you are, you can do search and replace in a text editor on the SVG file.
SVG files are human readable ASCII files (well, kinda readable). You'd need to use a text-editor that can do Regular Expression (regexp) search, like Sublime or TextWrangler on Mac (and maybe Notepad++ on PC?). In the regexp, you'd need to include a reference, something like
search for: [ fill:"(.*)" ]
replace: [ fill:"\1" stroke:"\1" ]
This is an example, it won't work literally.
That being said, there might me scripts or plugins or core functionality out there, that will give every path a stroke matching to its' fill.