There are a few issues.
All flash sites, have zero chance at search engine traffic.
Flash navigation can be a problem if the surfer doesn't have Flash intalled or the browsers to something wacky that makes them stop working like IE just did because of Eolas patent case.
http://www.webtechsig.org/Presentations/eolas.html
Due to the Eolas patent case , a new update to Internet Explorer will no longer automatically allow user interaction with plugins which are embeded in webpages. Think Flash navigation, music players (Quicktime, Windows Media, Real Audio), Java applets, etc. The applets will be usable, but only once you enable them, usually by clicking on them.
Lots of surfers don't like it and for those on dial up it's almost useless.
There are some things to be said for Flash because properly done it can add something to a website and using Flash for video clips works very well. However, I think for the average webmaster the cons outweigh the pros.