Apple - Dock Icons will not move in Yosemite

Did you try this?

Finder and Dock issues in OSX 10.10.1

I had the same exact problem and it was definitely caused by Pushbullet extension in Chrome. Disabled completely the extension, restarted the system and the dock started working. Don't know if it was caused specifically by the "Universal copy & paste" option being enabled or the extension as a whole, would have to investigate this further. Hope this helps.

In Terminal.app type:

defaults read com.apple.dock contents-immutable

If it comes back with 1 then

Make a backup of the plist file and then try this command to unlock the Dock?

defaults write com.apple.dock contents-immutable -bool no; killall Dock

Seems that pushbullet is the culprit (thanks @mysz). Specifically the chrome extension for pushbullet, uncheck universal copy and paste by visiting the extension's setting page. Do a restart and the problem should be fixed