I use quite a few web apps and desktop apps in this space, and have experimented with many more. I find Trello one of the most amazing apps I've used, both in it's general design and in the little details. Especially the little details. My expectations of web apps are generally not so high, so when, for example, trello remembers my input when I accidentally close something, it's a surprise.

The most recent discovery I made was that when you hover over a card and press the copy keyboard shortcut, it copies the card. Something I don't use much, but comes in handy every once in a while.

I think studying Trello's functionality would be great inspiration to improve your tool!