It is best to create a version of your main website optimized to mobile devices. The website created for smart-phones & tablets will display facets in a manner that will be easier for the mobile device users to navigate. Functionalities may vary from your main website which caters to desktops & laptops, but the purpose of the overall website will not be lost.
Think of the RAM capacity, internet speed plus data usage factors from user's perspective when accessing your website through a mobile device. Lot of images tend to slow down the loading factor and navigational speed of your website, causing the surfer to lose interest in your website.
Apple's IOS has no support for flash , thus making it impossible to access websites with flash content on any apple mobile devices. Even Android supporting devices offer jaded performance when it comes to flash. The good news is with the arrival of HTML5, the role adobe flash plays is minimal.
These days web designers are developing websites in wide screen format. These websites are good for desktop and laptop screens. But think about the size of mobile devices. Some users prefer to view stuffs on landscape, while others stick to portrait. These mobile devices too are customized to this functionality. Some even disable this auto-pivot function and stick to one specific layout. Unlike in the print world, designing for mobile devices is tricky.
One last vital factor to note is that, when creating custom widgets, scrollable areas & rollovers, think of how a surfer will browse websites with the usage of mouse compared to the swiping and clicking done with fingers. These facets should further be filtered through screen size factor of mobile devices vs. that of desktops/laptops. When doing UI for websites, especially for mobile ones, you will have to carefully go through each and every facet to ensure the user-friendliness of the site from these two different surfers.