For minGW, the only available backend is the DirectShow backend (dsengine), which will not support many codecs out-of-the-box. Installing codecs for DirectShow solved the problem in my case, except when the video does not include an audio stream.
We are now testing with a MSVC 2012 build, which includes both the WMF and the DS backend. WMF supports more codecs (but might have trouble with h.264). I will post the test results when they 're done.

I will look into the page you suggested.

For your question, I tried playing the videos many different ways including:

Custom iframe youtube based page that loaded a webm video

YouTube view app loading the same webm video

Called the W3Schools HTML5 Video demo from Tab Browser, Fancy Browser and a custom simple QWebView app

Made a local copy of the W3Schools HTML5 Video HTML and tried many different ways

I tried the Video Player sample app to load several good html5 video formats

All of the tests resulted with the same error message.

To extend my testing, I loaded the MSVC 2012 Tool Kit into my environment and all the videos play fine when I build using this tool kit. Therefore, this issue appears so far to be isolated to MinGW 32bit build environment.

How did you try to show the videos?

This page might provide some clues to the source of your error: http://qt-project.org/wiki/Qt_Multimedia_Backends