@Chris-Kawa thank you for your response! I know that there is no 64bit VS, and you are right about the 64 bit builds, I just don't know how to do it :) I managed to get rid of the problem written above by removing qtmain.lib from the lib listing, and VS builds the app succesfully. I just downloaded the 64 bit Qt version and will try it, hope it will be fine with MD and MDd settings.
// Disambiguate overloaded member function below with static cast
connect(socket, static_cast<void (QTcpSocket::*) (QAbstractSocket::SocketError)>(&QTcpSocket::error), this, &Network::socketErrorSlot);
I think that deserves to be in bugtracker, isn't it? Not good idea to implement new notation and use the same names for method and signal.