Remember that validators are pretty dumb, and just check your site against some rules they have. If they haven't been told about CSS3, for example, or vendor prefixes, they will go all wobbly at the knees, when in fact there's nothing wrong with these at all.
The validators are handy for alerting you to any serious problems that may affect page rendering. But if the pages render fine, the validator is otherwise useless. Getting worried about validator results when the page renders fine is misguided. The key is not to show clients these results, as they are likely to get freaked over nothing.
I admit I don't do "mobile" validator checks much, but I assume they are telling you about the more basic mobile devices. Those devices are pretty limited in what they can display, which is why some people these days are advocating "mobile first" design, which involves serving up a pretty basic version of a site that will work on the simplest devices, and then adding in more CSS for smarter devices like smart phones and desktops—excluding IE < 9, of course.
If you serve up something simple to simple mobiles first, you can avoid the horror of seeing your desktop site run through the mobile validator.