For clicking and targeting, you have the touch screen. Dota 2 is a 5vs5 player game. Controller can display all your enemies on the touch screen, just as you'd normally see their profile pictures at the top of your screen. You can click on their profile pictures to target them when they're visible on the map etc. As for the movement, I think movement could be much better with a game controller. You probably can not click on a map and wait for your hero to go to the spot you've clicked on, but you can direct him there with one of the touchpads.
I think another big problem would be using the shops. In the current style of the game, I don't think it'd be possible to use the shops with a controller because there are just too many items. Having said that, if Valve really wants people to play Dota 2 with a game controller, I'm sure they can implement some changes. Currently in game items are seperated in categories. They can use that wheel chat idea with the shop and let players browse through the items. I'm just brainstorming. It can be done. 2 different UI implementations for 2 different platforms, but one game.
I'm not saying these changes or even playing Dota 2 with a game controller would be ideal, but I think it's doable to make the game controller friendly. But there's no way in hell I'm going to give up on my mouse and keyboard for Dota 2 and most of the games that I play (apart from the sports games).
[1]http://www.rahulsood.com/2010/07/console-gamers-get-killed-a...