Doing all this gets it working when compiling IN RELEASE MODE.
When you are compiling using debug mode, the program will shut itself down right away. To be able to use debug mode, you need the qwt library compiled the same way. Sadly, the makefile has got serious issues, and if you compile as debug it will overwrite the release library..
To fix that, open up %QWTDIR\src\Makefile.debug and rename all the output files to qwt5d.* instead of qwt5.* (e.g. qwt5d.lib instead of qwt5.lib). This creates a debug library alongside the release library. Copy the DLLs created to the %QTDIR%\bin so that your programs will be able to see it (since that directory is in the path variable).
I know this is annoying, but (IMHO) handling of these MS specific problems is something that has to be added to qmake. If you have a commercial license please add a change request to Trolltechs task tracker.

Uwe