there should be tiny movements between 3' to infinity because that area of the scale represents a HUGE range. But still if you are using spot metering and point at something a couple hunder feet away I would hope it goes to infinity.
Here is a test you might try to see if the scale is off and the lens is still focusing or the whole thing is foobar'd...on a very distant subject that should be in the infinity range of the lens, run a test shot with AF on then turn it off and manually focus on the same target but crank the focus to infinity...see if that makes a difference in the distant object.
I have read many lenses from many different mfg's can have probs so it's not unreasonable. Still one should expect perfect functioning from a new item.
Funny, I just did the exact same test as you suggested - with weird results.
I AF on a building a few hundred yards away (which read a little over 3 ft). Then took off AF, , manually set to infinity and took the same shot (3X each).
The AF shots were in focus, the infinity shots were out of focus. 
Unless I'm missing something, this lens is having focusing problems - manual and AF!
I tried it on a building a mile away -- same results!
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