I found a reference on another site regarding spining carbon arrows. The author of the thread stated that there was a stiff side to his Gold Tips, and that it made a difference in tuning. How do you tell the stiff side, if there is one? Do you just spine the shaft at different points around the circumference?

Yes.  I have spined many different brands of carbons. Some have different spine readings at each fletch. Some shafts that were rated .400, when tested came in at .425 and so on. Carbon Express tested the best.

The "stiff side" he is likely refering to is perhaps where a layer stops/starts (?). I've also read where some people plug the ends and float them, supposedly any heavy sides will end up down, I don't know much about that. I bare shaft all mine first. If you have most of them going to the same spot and a few that won't, take those few, and try rotating the nock a 1/4 turn and retry. Keep going 1/4 turns and see if it will come into the rest of the group. Once they're all going in the same place, then fletch them.
If they're already fletched, and the arrow won't play nice with the others, rotate the nock to a "new" odd feather and re-try. If it just won't group, change out the nock and see if it mkes a difference.

The Cupcake tester says there is a definite stiff side to Grizzlysticks.

With the Grizzlysticks ya can actually see the thicker side. I never liked them but I kn9ow guys love them. Ya can roll on a flat surface and they will stop on the thicker or stiffer side, I agree the the carbon express are the most consistent of those I have tried. Shawn

I also do not try and find the stiff side if there are and I too think Carbon Express the best carbons all arrows weigh the same fly the same they are the most consistent arrow shaft I have tryed and I have tryed most the new weight foward Cx 250 shaft with 100gr brass insert cut to 31" flys excellent out of my 54 lb Stealth and also out of my 61 Lb Kwyk Styk  

My first batch of Grizzly sticks had stiff sides that were easy to find by spinning.  The next set had no such spots and testing them out on a spine tester by myself and with  peer review by two others found the same.  There was a variance of only a couple pounds around the shaft, and we turned each shaft numerous times (not just three) to see the variance.  

The first batch were made in the US, the second batch were supposedly made in China.  They BOTH fly great for me.
ChuckC

Oh yea, gold tips will have a stiff side.  I have mailed back a few to them to make them replace over it.

Thanks, guys. Sounds like a sometime thing, but well worth a look. Appreciate the comments.