The various browser vendors- Apple, Microsoft, Google, Mozilla, and Opera- all have differing support for HTML5 video. There is an interesting Wikipedia article that explains the problem quite well
At present, there is no one video format that will play in all web browsers and political considerations among the browser vendors make it unlikely that this will change. A site might need as many as three video files- mp4, Ogg, and WebM- for universal support.
Camtasia for Mac and Camtasia Studio currently can output mp4 video files. If you post those on a website with the HTML5 video tag, many visitors would not be able to view them and would have to fall back to a browser plug-in. The whole idea of HMTL5 is that plug-ins are no longer needed.
We do support HTML5/mp4 on screencast and this works for the 15 million iPads and 100 million iPhones which have been sold, and you can easily edit our HTML files to add the HTML5 video tag.
Hopefully we'll see improvements both on the tool vendor end (such as our products) and the browser end of things to make HTML5 support easier and more useful.