What is causing this chain clicking noise? The click only happens when the chain is moving in certain locations. If the gear is low it happens every rotation and if the gear is high it happens 2 or 3 times per rotation of the pedal.

I am trying to figure out if the chain is stretched or somthing is wrong with the cassette.

To explain this more I have uploaded a demostration video of how it sounds.


                
            

This happens on multiple gears at different locations on the chain. It happens more than once every turn of the pedal depending on the gear. 

Update: measured chain for stretching and looks like no issues.

UPDATE: Fixed by adjusting the cable tension using rear barrel adjuster about half a turn.
A couple of things I see:  


I think your derailleur is a bit out of adjustment and is "leaning" towards the lower gears.  It's grabbing on the ramps of the lower gear as it goes by.
Your B screw adjustment is a bit too far away from the cassette.  I would try to get it within a link or link and half.  It looks from the video that you are about 2-3 links away.  See section 4 of this link: http://www.sheldonbrown.com/derailer-adjustment.html


Lastly, is it possible that 9 speed chain (or less) is on that 10 speed cassette?  If the chain is too wide, it would have the same symptoms (grabbing the ramps)