The new app supports many parts of the EPub3 spec, but according to the release notes there are still a few features which have been left out.
Update: Adobe goofed on the release notes. They now say that they forgot to remove from the release notes issues which had been resolved or fixed in this release.
For example, Adobe DE 4.0 does not support embedded audio or video, and it is also lacking support for basics like right to left languages (Arabic, Hebrew, etc) . The search function is incomplete, and the app is also lacking advanced rendering features (such as knockout, overprint, and non-separable blend modes). And last but not least, mouse wheel scrolling is officially not supported for Epub3 ebooks.
And it gets worse for Windows users. This version of the app is also lacking MathML support, and it does not play well with IE9. The Windows app will also ignore several lesser features, including wbr, which is used to indicate where to split a word when hyphenating.
In addition to the incomplete support for Epub3, several bugs have also been mentioned in release notes, including memory management issues caused by large image files and other issues.
While I would normally encourage readers to rush out and get the new app right away so you can play with it, I think it might be better to wait until more of the bugs are worked out and more features are supported. But if you would like to try Adobe DE 4 and experience the joy of Epub3 for yourself, you can download the app from Adobe.