Now using a 3D API to do rendering handles a lot of resolution dependence issues. However, user interface details are still something of a problem. Usually scaling user interface textures just looks ugly, and not scaling them can also look just as ugly.
Right now I'm thinking about using SVG to describe my user interface elements. That way I only need it to work at a few display ratios rather than worry about different resolutions. Right now I'll support 4:3 and 16:9. I might go crazy and support 3:4 and 9:16 too.