Error downloading updates "An error occurred during the update" on Steam is very common. This error is related to updates in Steam. This allows you to optimize a large number of internal processes. These innovations should help in the gameplay, but not always everything runs smoothly.
HOW TO FIX?
1: Go > My Computer > Steam > steamApps > downloading
2: Highlight the "downloading" folder and delete it.
3: Re-open your Steam application again, you'll see that Dota 2 is on 'Update Status'
4: Double click on Dota 2 and it will update itself until it finish, you could play Dota 2.
Also try changing your game download region. This can be done in the settings (Steam. If this does not help you, then you need to completely remove DotA 2 and install it again.