Did it in two commits, one removing the C++ asserts:
https://github.com/naucoin/Slicer/commit/e52351dcba2588e885ef8054aa1c89b91c024aea
One removing Q_ASSERT:
https://github.com/naucoin/Slicer/commit/f1ad1d91fb0c2cfc2e3e4e56db7bbcc39c1be011

Ran make Experimental uploads as was making changes, and caught a few logic errors. Last one after rebasing:
http://slicer.cdash.org/viewTest.php?onlyfailed&buildid=179119
The volume rendering scene close test is passing now, though it prints out an ERROR via the qCritical() call. Others are also failing on the trunk.

Posting to the dev list for more feedback, especially on the qMRMLSceneModel

What I found useful and what makes the log messages consistent is to prefix all messages from std and Qt with class and function name, like
qCritical() << "qSlicerClassName::methodName: Error message";
I use this throughout my code, because the vtkErrorMacro and siblings all prefix the messages with the class name, so this way the error messages look very similar (which makes them easier to read), and immediately knowing the place of error also helps.

I also have been thinking about the std::cerr usage where there is no VTK object whatsoever that can be used for vtkErrorWithObjectMacro and such, and found a macro named vtkGenericWarningMacro. I haven't had time to look into that, just made a note about it, so this might not work, but is worth noting, in case it does.

Should all the qCritical print outs use the ERROR string?
Yes - but the developer shouldn't add the text

Should there be more data on the file/method names in the qCritical strings?
Yes - but that should be automatically done

A lot of the asserts in the vtk files were in places where I couldn't
use vtkErrorMacro, so I just used piping to std::cerr where the
vtkErrorWithObjectMacro wasn't working either. Is there a better way?
No - the approach reported by Csaba should be investigated.

Waiting Slicer transition to Qt5, to associate more information with qCritical/qWarning/qDebug, the QMessageLogger class now available in Qt5 could be backported into CTK. See http://qt-project.org/doc/qt-5.0/qtcore/qmessagelogger.html#details

Rebase topic branch and integrate on Mar 6 or 7, 2014.