With Responsive Web Design building a site Mobile First is an excellent way to build site infrastructure, serving the least amount of code to devices that often have less bandwidth and building up from there.
A problem is that IE8 and below do not support media-queries, thus when users visit a Mobile First site using IE8 they are served only a mobile site on a desktop browser. Whomp whomp! Personally I’m all for dropping support of IE8 and not worrying about it (which is usually what I do) but sometimes you must support IE8 whether you want to or not. Microsoft will no longer support IE8 as of April 2014, and while that’s great to hear it does not mean IE8 users will be upgrading.