Apple - Can't rearrange Dock icons

So turns out, this problem extended to other parts in the system, namely: Xcode.
After some back-and-forth communication with Apple's support case team, the crash problem in Xcode turned out to be ibtoold and pboard processes are malfunctioning. They said it's a clipboard set of processes, and if I have any clipboard-relevant apps - they might be clashing with them.

So the only possible culprit on my system was CopyClip.

To make sure that was indeed the problem, I quit CopyClip, and restarted the processes, then restarted Xcode:

killall ibtoold pboard

And it worked. I made sure that was indeed the problem by starting CopyClip again, then running the same command again - and the problem returned. I then fixed it once more.

I figured the problem might be the same for the Dock, so I killed it:

killall Dock

And voila, it was functioning again!

TL;DR: Applications that provide special handling for the clipboard, such as CopyClip or PushBullet's "Universal Copy and Paste" collide with processes necessary for Xcode and Dock to function correctly. My problem was resolved by disabling or getting rid of that app and restarting.

I was experiencing the same frustration with El Capitan (10.11.1), but discovered that the solution (in my case) was simpler than inserting code in Terminal or Xcode.

I found that if I delayed beyond the initial click I was presented with the drop down menu and was unable to drag. But, if I clicked and tried to move immediately the menu did not appear and I could drag the icon. If I kept the icon too high in the Dock the other icons would not open a space, however if I held the icon lower in the Dock they would separate, and I was able to drag and rearrange.

I hope this is helpful.

try this way,delete the file ~/library/preferences/com.apple.dock.plist and restart. your dock, spaces and expose will be reset to the defaults. try rearranging the dock icons again.May be it will fix errors.