Don't Use Flash
Flash isn't dead yet, but in the words of Monty Python, it's "pining for the fjords." In a world that increasingly revolves around browsers in mobile devices, Flash has become irrelevant; it doesn't run on the vast majority of devices, and since Adobe has abandoned mobile Flash development, it never will. Apple had its own reasons for not wanting to support Flash on iOS devices; the company learned from Microsoft not to allow other vendors to set de facto software platform standards for its hardware. However, Steve Jobs was also correct in his famous Flash missive: Every mobile version of Flash that Adobe demonstrated gobbled battery power.
If you want to show video, you can (and should) use HTML5 and the H.264 video format, because almost all modern devices, whether desktop or mobile, contain hardware chips that decode and play back that video format with minimal power consumption. Major sites containing embedded video, including news sites, Facebook, and YouTube, serve video in either H.264 or Flash as needed, often using H.264 as the primary, with Flash as the fallback for older devices and browsers.
There's probably a new, special circle of hell for designers who bamboozled their restaurant clients into using cutesy Flash-only sites after the release of the iPhone in 2007. The main mission of a restaurant site is to bring in customers, and a site that prevents people from looking up information about the restaurants' hours and menus is a total failure. I can only imagine how much revenue the restaurant industry has lost over the past years to such boneheaded sites. If you're stuck redesigning such a site, immediately implement a non-Flash page or two with the business' basic information while you rebuild the rest of the site.
Along the same lines, another "don't" is commonly associated with Flash-heavy sites: Avoid including a splash page that does nothing except show some allegedly fabulous animation, and needs a click from the user to load the "real" site. Designers may gush about "branding statements" and convince businesses that they should love a splash page, but users will hate it. Splash pages keep users from seeing the content that drew them to the site in the first place. If your site has a splash page, get rid of it.