Should I be able to 'manually' rotate the headset?
Most likely you are describing a spacer, but it is not clear.

The spacers should not spin. If they do, it's a sign that the bearings have little or no pre-load and the head set will be loose.
Couple possible causes

The pinch bolts were not loose when the top cap was tightened.

You are missing a spacer.
If you want to lower the bar, you move a spacer from below to above. Someone may have removed a spacer to lower the bar without replacing it above the stem.


Internal view of head assembly

Note: There must be a gap between the top of the steerer tube (fork) and the top cap. If not, the cap bolt cannot pre-load the bearings and a spacer needs to be added. It can be added above the stem if desired. Alternately the steerer can be cut shorter.
How to fix:
(Should take no more than a few minutes)

Back off the cap bolt a couple of turns. Loosen the pinch bolts on the stem until it can easily rotate.
Tighten the top cap bolt (not too much). This sets the bearing pre-load.
Tighten the pinch bolts.

If this does not work

Leave the pinch bolts tight and remove the top cap.
Check for a gap between the top of the stem/top spacer and the top of the steerer.

If there's no gap, go to your LBS and get a spacer or two (a few dollars at most).

If there is a gap, and the spacers below the stem are still turning, something is very wrong. Check that the threads on the bolt and star nut are not the problem.




Refer to this wikibook for instructions.