Recently noticed my headset was loose, so I tried to tighten it.
Couldn't get all the play out of it until I tightened the top cap nut very tight.
It still turns freely, but it seems I shouldn't have to tighten it down so hard and I don't remember this happening before.

You have too loosen the stem before tightening the top cap.

Yes I always do that.

Ok, I'd take it apart for a quick inspection just to make sure everything is in good order on the inside.

Have you changed anything recently with the headset spacers? A tight cap and loose headset usually indicates that the cap is bottoming out on the fork steerer tube (or the star fangled nut has slipped).

That was my thought: the star-nut may have slipped. I have had five CK headsets on my various bikes (including on two tandems) for many years, and the only problem I've ever had is the star-nut slipping. IMO, the star-nut is the weak link in an otherwise well designed Aheadset/threadless system.

You can buy inexpensive star-nut setters from Nashbar, Performance, etc. Nice to have in the toolbox, and automatically sets the star-nut at the correct depth. (Note that they don't work too well on Santana 1.25" steerers, as they are made for 1.125 steerers.) If your star-nut is slipping, best to just get and install a brand-new one. Once they start slipping it's hard to get them to stay put.

Sometimes headsets need a thin stem spacer (ie: 1-2mm) inserted under the top cap/cup of the headset itself. It's not specific to CK. You can pick up the phone and call them to verify.

I've had trouble with my older WoundUp carbon fork and steer tube. I have to tighten the CK headset quite tightly once in a while. I think what's happened is that the carbon steer tube has become a tad smaller with time and wear and is now under spec. The stem, tightened to spec, will slip on it after a while, particularly after fast and bumpy descents. I've tried a couple different stems on it. Stems with less bearing surface seem to do best. I'm not that anxious to buy a new fork: kind of spendy. The LBS has looked at it - no solution.

I think someone does not understand threadless headset Mechanics.

top cap is just along for the ride after you tighten the stem pinch bolts ,

so as to hold the pre load adjustment.. created , by lightly turning the top cap bolt,
while everything underneath it is loosened..

I did notice that the nut is very close to the top of the spacer and was possibly bottoming out the top cap.
From what I remember the stem came with epoxy to glue whatever holds the nut in.
I put a taller spacer on and it did not make any difference.
It seems that something is bottoming out but I don't know what.
In the mean time it seems to be ok, but its still bothering me that something isn't right.
When I have time I need to take the whole thing apart.

I had that exact problem with my Specialized Tarmac, couldn't get the play out of it. I took it to the shop and they replaced some of the parts and added the thin washer.
It was thinner than 1-2mm, more like 0.1mm.
Maybe over time things have changed on my tandem where I need a washer.

Yep

I found the exact opposite to be true... that stems with more surface interface area hold the steerer better than those stems (ie: 3T ARX) with less gripping area. This should make rather obvious sense. I have had zero slip problems with Ritchey 4-Axis stems @ the mfr torque spec, whereas the 3T ARX was problematic. You can augment the stem grip by using carbon grip pastes. So there you have it... two solutions to zero for your LBS.

I use carbon assembly paste. It's a carbon steerer after all. One of the stems I tried was a Thomson with a greatly cutout contact area. That worked better, but was a 0° stem and I wanted a 17° drop. The best stem so far is an Eleven81, which has a short body, about the same as the Thomson and is 17°. I stacked washers on top of it to make up the difference. It's possible that the increased PSI from the lower surface area helped, or that it does not grip the steerer in the worst worn area. Anyway, that's what works the best.

I have a ~.5mm plastic washer between stem and top cap. Should there be another, thicker washer? If so, what would it do?

Dispersal is the proper aim + grip surface area, whereas "increased PSI from the lower surface area" is the last thing you should want for any attachments to carbon components. Any deformation of the carbon is a sign of crimping damage. A stem with narrow gripping area may dig into your steerer and provide temporary grip, up to the point where the steerer is decapitated.

Washer spacing between the headset and stem is not the area I was referring to (in earlier posts).

[QUOTE=twocicle;16491060]Dispersal is the proper aim + grip surface area, whereas "increased PSI from the lower surface area" is the last thing you should want for any attachments to carbon components. Any deformation of the carbon is a sign of crimping damage. A stem with narrow gripping area may dig into your steerer and provide temporary grip, up to the point where the steerer is decapitated.

Washer spacing between the headset and stem is not the area I was referring to (in earlier posts).[/QUOTE

Torque wrench up to prescribed Newton meters takes all guessing away