I have. It used to use X11, I saw even more complaints then.
There aren't any competitors, however, so people use Mathematica.
I use high-end expensive that are Qt-only too, but I would gladly switch if there were other options, because Qt is buggy, uses non-intuitive non-standard UI, exhibits poor performance due to impedance mismatches between the Mac and Qt event/threading models, and ultimately decreases overall utility of the UX.
Can you give me an example of the "non-intuitive non-standard UI"?
This may well be true, but it's quite possible it's just the developer was lazy and didn't do all the effort to make it look native.
Edit: in fact, I'll give an example: VirtualBox - it does look crap on OS X, but that's because the developers obviously didn't make any effort to make it look native. They've got icons in tabs pane buttons and huge toolbar buttons along the top (which isn't a unified toolbar btw - which would make it look more native), which goes completely against the way OS X apps tend to look.
VirtualBox, IDA Pro, Google Earth (in fact, everything from Google that uses Qt), EAGLE (PCB software), OpenSCAD, QGIS ...
I've literally never been fooled by a Qt app -- a Mac user can spot that hot mess from a mile away. It's not just a matter of visual layout and UX, although that matters and always falls somewhere between subtly or completely wrong.
The controls also tend to lag at weird times, behave slightly strangely, demonstrate unusual font metrics, etc. The apps tend to exhibit bugs related to menu bar event handling, window management, on and on, and crash more than any other apps I use daily.
This isn't a huge surprise given that Cocoa is designed to be the first and only gatekeeper between events, the OS, UI controls, and Cocoa's main event loop, and most of what makes Mac apps a Mac app has to do with the APIs and integration that you lose first-class access to once you deploy Qt -- that includes 'simple' things like UI layout metrics, which Qt has to re-implement.
I abandoned almost all those Qt apps on my list above. I even dropped EAGLE, despite being "native", in favor of Altera on Windows, which I paid a hefty premium for in no small part because it wasn't a pile of broken UX, Windows or not.
I still use IDA Pro, but the minute http://www.hopperapp.com/ can replace my IDA Pro usage, I'll switch in a heartbeat.
Although having looked at hopper, I must say I'm not convinced it seems any more native than a Qt app on OS X could look if work was concentrated with this goal in mind. So as I said in my VirtualBox comment, I think that while indeed it is a Qt deficiency that apps don't look native straight from the compiler, more work could be done by the developer to make it more native-like.
I've seen controls acting weirdly but only QPushButtons - that seems to be regarding the hit-test area - we've had to sub-class a lot of them on OS X to fix this by making the hit test area bigger which is annoying. There's also a pretty bad spacing/padding/layout issue as I alluded to in another comment.
I agree with the event stuff as well - definitely one of the biggest things which affects us is that sometimes mouse/keyboard events don't get sent to the app if the app isn't active or the mouse isn't over a particular window. Debugging through Qt, it seems that Qt never gets the event from the OS, so we have to install event filters for all windows and intercept them which is crap. We've also seen weird stuff like key release events being received before key down events - again debugging through Qt, it looks like an OS X issue in that that's the order they come in from the OS, but again, without a native version to compare to, it's difficult to tell or test.
Generally the crashing of our apps is due to graphics drivers or memory allocation issues (we deal with huge amounts of memory), and I'm not aware of Qt itself being the result of any crashes on OS X for our apps any more than other platforms, but I guess without a native version to compare to, it's difficult to say - but Qt is very rarely the cause of crashes in my experience and I generally develop for Linux and OS X.
Somewhat off topic, but does anyone know how Adobe does their cross platform interface? It doesn't feel like native Mac OS UI, though I think it works pretty well.
