I think you underestimate how much is going on in an app like Gmail

I've no doubt they do all kinds of clever things behind the scenes, from detecting things like malware and spam to all the analysis Google do for their own purposes.

Still, relatively speaking, I don't think the front end for an e-mail client is very complicated. And there's nothing wrong with that, because it doesn't need to be: its job is to manipulate a small amount of data (from the user's point of view, with a simple structure, which doesn't change very much and doesn't have a lot of dependencies.

This is all true of most major web apps, as far as I can see.

..."real-time assistance as you navigate the information, context-sensitive UI, [and] task-specific controls" in the browser. Those problems are mostly solved.

Don't you think "mostly solved" is overstating the case a little? Even web apps whose UIs we might call mature or advanced today rarely offer more than what desktop WIMP UIs were doing 10 or even 20 years ago. As you mentioned, even common operations like editing formatted text are often still below par. Truly task-specific UIs, the equivalent of say a three-way diff/merge tool or a space flight simulator game on the desktop, seem to be extremely rare in web apps.

Startups aren't what drives tech innovation in markets?

Start-ups can certainly drive innovation, though obviously this particular forum has a built-in bias and I think a lot of posters here tend to overrate the importance of any one start-up or of start-ups generally.

However, I don't think whether or not we've heard of start-ups means very much. It's a big world, and most of us will only ever see a tiny fraction of it. Lots of the innovation happens in small businesses that help larger businesses or other non-consumer fields like academic research or government departments behind the scenes. These things don't tend to be very visible to the general public, and probably won't get you on the front page of HN or written up on TechCrunch. Plenty of these projects involve developing desktop apps.

What is the most recent desktop app that you could call innovative, apart from pushing the envelope on graphics?

I can't give personal examples from my own work unfortunately, so instead let me ask you this: have you been to a movie lately? Did you notice all the CGI special effects? Not the robots and zombies and futuristic home automation, the other ones. The answer is probably "not even close", because the programs the SFX wizards use to create those effects are now so powerful that the results really do go unnoticed a lot of the time, as they should. These things are done with a vast array of bespoke software that is evolving all the time, some of it off-the-shelf but a significant chunk built in-house for major projects. And they're not building web apps. (Most of the time. ;-))

Perhaps the habits people have acquired around downloading and installing mobile apps will end by triggering a renaissance in desktop applications. But I won't believe that I until I see major new applications being built this way.

I tend to agree. I fear that ship has now sailed, but it would be nice to think that the groups behind the significant desktop platforms could still come up with a sane way to install and update applications.

It's crazy that in 2012 (just...) we still rely on each application's installer/uninstaller/package manager/update process to copy files into basically arbitrary locations, some of which may be shared with other software, set up hidden details like registry entries, even hack around global system configuration or perform dark magic for product activation/DRM purposes. And then we expect to install more than two things and have them play nicely together, and then uninstall in some arbitrary order and still have them play nice together.

Here's hoping 2013 will bring something better!