Last I saw, QT's GPL/LGPL license required you to open-source the code that was statically linked to it. That wasn't much of a problem for desktop platforms, as you could just package up all of QT into its own QT.DLL (or the equivalent) and link to it dynamically. But this isn't allowed on stuff like iOS, so you were required to buy a license for those.
And it's a bit of a misconception that LGPL requires statically linked things to be open sourced: in that area it only requires that the LGPL components be replaceable (and the source for the LGPL components be available). In the context of static linking, that can be done by releasing pre-link binaries (object files) with instructions for linking them.
Of course, that's likely more work than just making the source available under a proprietary license (ie: provide source code so LGPL components can be replaced).
If you're using Qt GPL components, then yes, you'll need to open source your application (or pay for a Qt License)
edit: can't comment any further currently, I will try to answer everything once I'm unblocked.
Some of the language bindings that aren't maintained by Digia are still GPL, though. An example of this is PyQt, and the PyQt team's intransigence on the GPL is why PySide exists.
QT is Apple QuickTime which some consider as the worst Windows software ever created.
I was guilty of mispronouncing it too, until Qt 4 came out and they released that goofy "Qt 4 dance" video.