Web sites generally required full Flash 8 or Flash 9 support.
Phones come with Flash Lite which is a subset of full Flash, and it works with local/standalone Flash Lite apps on the phone.
With some phones and their latest updates, there might be a newer Flash Lite version (like Flash Lite 3.0) and corresponding updated browser support. It works somewhat better, but is still not the same thing as full Flash for PCs and browsers in a PC, so many web sites won't work, if they depend on full Flash.
There's nothing much you can do about it, except ask Adobe to make Flash Lite more compatible with full Flash, and then wait for device manufacturers to incorporate that in their phones (after Adobe has done their part).
Other than that, you can also ask web site owners to create web sites that do not depend on technologies that only work on PCs.