Recently on my MacBook Pro when I launched DOTA 2, the dock was showing and the menu bar, buttons were being cut-off and the game was hard to use. The issue seems to stem from how Steam sometimes launches the game client.
The fix is rather simple and worked for me.
- Open up the Steam client
- Click the Library tab
- Right click on Dota 2
- Select Properties
- Click on the General tab (it should be selected by default)
- Click on the “Set Launch Options” button
- In the box that pops up enter -fullscreen