I tried building on windows and got this:
error: No rule to make target 'c:/Qt/projects/bitcoin/src/leveldb/libleveldb.a', needed by 'debug/bitcoin-qt.exe'. Stop.
The build-mws.txt, README_windows.txt, and readem-qt.rst files do not make any reference to building the libleveldb.a file outside of the bitcoin build.
I did not separately download and build the four items listed in build-msw.txt, but none of them are leveldb. I downloaded and installed the dependencies as instructed in the readme-qt.rst file.
This led me to lines 100-104 of bitcoin-qt.pro "# make an educated guess about what the ranlib command is called". I'm looking up this "ranlib" thing...