If you navigate within a Flash object, the standard backtracking method takes you out of the multimedia object and not, as expected, to the previous state. Link colors don't work. Given this, you cannot easily see where you've been and which links you've yet to visit. This lack of orientation creates navigational confusion. Users are thus forced to read text in the designer-specified font size, which is almost always too small since designers tend to have excellent vision.
Flash reduces accessibility for users with disabilities.
In general, Flash integrates poorly with search. Internationalization and localization is complicated. Local websites must enlist a Flash professional to translate content. Also, text that moves is harder to read for users who lack fluency in the language. If Flash was cheap to produce and if all content creators could make a Flash object as easily as they write a standard Web page, then perhaps many of these problems would be alleviated.