Qt is written in C++. GTK attempts to do object-oriented code in C and the result is a mess of explicit casting and macros. Seriously, most GTK C code looks horrible and is far less terse than the equivalent Qt program. This is mitigated when Python or Perl is used, but then you're sacrificing speed. With Qt writing C++ is basically as easy as using Java, C# or any other 'modern' language. All of the nasty stuff is taken care of. For example, Qt code is generally cross-platform.
Its signal and slot system is also very powerful. For example, you connect a button's click() signal to the QApplication's quit() slot, and the button will cause the app to close when clicked. These signal/slot pairs can even be set via the Qt Creator IDE, just like Visual Basic! Or you might start up a webpage download and assign a slot to handle the signal sent when the page has been downloaded. Qt's signal/slots are introspective and modifiable at runtime, and you define new signals and slots just like you define new methods for a C++ class. The drawback there is that Qt programs require a pre-processing pass by moc (the meta-object compiler), in order to generate meta-data for runtime signal/slot manipulation, and to offer some syntactic sugar around Qt's features. As a side-effect, Qt adds syntactic sugar for features some might find questionable, for example adding a foreach() loop for lists.
The build system, qmake, is quite simple: you list your source files, libraries and headers to link in a short configuration file (qmake can even generate this for you). qmake then generates a makefile from this data. This is useful as it also includes the 'moc' pass, but can be constrictive in some cases. You are, of course, not obligated to use qmake in your Qt project.
As far as widgets go, Qt's are comparable with GTK or any other toolkit out there. Qt does a better job of looking good on non-Linux platforms, such as Windows. It has a simple but flexible widget system that is much easier to use than GridBagLayout or any of Swing's more poweful layouts.
The main issue with Qt was that, up until recently, it was licensed under the LGPL and before that, it was under the restrictive 'Qt license'. This is no longer the case, so jump in!
Yes, because people love to read long pages of text and never just click the first button at the bottom of the dialog. More importantly, plenty of Firefox users don't know they're using Firefox, or don't care, and won't know how to react to such security notices.
The first notice is much simpler: users will recognise that they are 'upgrading' to a new version, almost all will allow it, and people who don't like the awesomebar or something have the option to deny. The second notice is just confusing to novice and casual users.
Any sufficiently advanced technology is indistinguishable from a rigged demo.