Mobile web design's new approach is responsive design, but one of the biggest challenges for web designers and their clients is finalizing the layout or wireframes as to how the website will look.
Some of the other challenges we need to overcome to build successful websites are:
Responsive design takes more development time than building other websites
Scaling images reduces image quality because scaling is based on screen size and not context
On smaller devices, using navigation menus becomes a challenge
Browser compatibility becomes an issue; because of older browsers, the support of media queries becomes limited
Building complex websites becomes a tedious task with this technology
Development cost is higher
Response time of the website becomes slower because of the much larger size of the web page
The loading time in mobile devices is increased while downloading the desktop content that is not even displayed