Using Adobe Flash within a website at one time was the bane of search engine visibility. Although Flash sites were often dazzling, highly interactive, and dynamic, they were not adequately being indexed (if at all) by the big search engines. Here's a flashback article from 2003 on this topic.
Adobe has just announced a plug-in available to Google and Yahoo that allows their search engines to act like a user clicking thorugh a flash website. This seems to be the latest effort at indexing Flash sites but some say that obtaining a high search position willl still be difficult because of the inability to provide direct links within the flash site.
For example, if a blogger finds a page in a flash site that is several clicks deep she will not be able to link directly to that page in her blog. Instead, she would have to link to the front page (the page that loads initially) and instruct the user how to get to the deeper level page. Yuck!
So, if you want to build a highly interactive website, use AJAX and Web 2.0 technologies instead of Flash. You can still use Flash movies embedded within your site but don't let the Flash handle your website navigation. I'd like to caution, though, that AJAX and Web 2.0 have their own issues which I'll tackle in my next post.