Helped by the testing by vgarvardt, many issues and possible features have been fixed or implemented in the last two days. Here's an incomplete list:
Implemented (and later fixed) proper close-to-tray
Marking a folder as read marks all its children
The reset filter button works like Akregator's
The tray changes its icon when there are unread items (and shows a count in the tooltip). Icon work needed, though.
Double click on a post opens in external browser
Default refresh period is configurable (no UI yet)
The feed tooltip shows unread count
Window size and position is memorized
Position of the splitters is memorized
Toolbar titles are now reasonable (never tried to right-click a Qt toolbar before)
Better templates for feed and post layouts
Unread items/feeds are now shown bold
The about window has the right title and icon, and doesn't appear in the taskbar.
There is almost certainly going to be a release tomorrow.
And here's a picture: