Manually adding a new Qt version fails silently if compiler is incompatible

From http://qt-project.org/forums/viewthread/21404/

Scenario
Previously, I manually added Qt 4.8.3 and MinGW GCC 4.4 into Qt Creator (neither are in my PATH)

I built Qt 5 from source, using MinGW GCC 4.7 in my PATH. Then, I tried to add qmake.exe to Qt Creator

Main Issue
The attempt to register my newly-built Qt 5 failed silently. Qt Creator did not:

1. Register my new qmake.exe, or
2. Provide an error message

(I'd expect (1) to happen, and (2) as a fall-back... but neither happened)

Workaround
Removed MinGW GCC 4.4 from Tools -> Options -> Build & Run -> Compilers. Qt Creator then registered my new qmake.exe as expected.

Further issues
After that, I re-added MinGW GCC 4.4 and restarted Qt Creator. But, my Qt 5 installation was flagged as faulty, and Qt Creator said

qmake does not exist or is not executable