I have been noicing that in aech group I shoot I get 2 groups of the same size about 1/2 to 1 ince appart from my box stock Bushy V-Match with various loads using 50 to 60gr bullets. It seamed to me that this could be caused by poor contect between upper and lower receivers. So, I put a small shim of about .025 inch on top of the Accu Wedge and it made a big difference in the groups.... no doubles. Now, I'm interested in hearing if any of you have found that using an expandable rear take-down pin can make a reasonble decrease in group size. What say yea? Since I am getting 3/4" groups or less when I don't get double groups maybe I shouldn't complain.

Barrel harmonics is a big key to where a barrel will put a shot down range.  As a bullet is fired and starts to spin down the barrel, the barrel starts to circular whip.  Due to barrel pressure, bullet weight, and speed/time of the bullet in the barrel, different types of bullets will leave the muzzle at different end placements of the muzzle whip (sights/receiver pointing at the same place).

By dampening the amount of movement of the barrel start point (the receiver fixed point), the less chance of the end of the barrel being elongated in its whip. This is why bolt-action rifle actions are glassed into the stock to achieve better performance in accuracy.

Now on your rifle, if you go from 50gr to 60gr bullets, the POI of the bullet should/will be different in regards to your aim point threw the scope/sights.  Granted that the added shim has tightened the upper to the lower (tamed variables in the barrel harmonics upper movement on the lower), it will not change the fact that the two different rounds act differently in the barrel (peak pressure bullet placement, movement of mass down the barrel) and the end point whip will be in a different point of whip/circular cycle as the types of bullets exits the muzzle.  

Personally, I think that you may have missed a major factor, and that being the end crown of the muzzle, or throat bur of the chamber.  New barrel muzzle crowns/throat cuts have a tendency to have a slight bur that will affect the bullet.  In time, the burs are polished out by the ammo, and resolve the problem.  

Chances are that either a muzzle bur affected one type of ammo over another type simple because the bur may have been at a place in the muzzle that was more sensitive to a certain barrel harmonic end placement, than the other type of ammo was producing.
Or, a chamber throat bur had more affect on one type of bullet to another type (jump to lands before engagement).

The real test is to pull the shim, and then re-check the rifles performance one again to see if you get the same results.

Thanks for responding, but.......maybe I wasn't too clear about what my question was. I understand and agree with what you wrote, but my problem does not deal with groups containing different weight bullets, but with groups containing 5 identicle loads. Some (many) 5 shot groups will contain 3 holes with a center-to-center distance of 1/2 to 3/4 inch and the other 2 holes will be the same center-to-center spread but be as much as 1 inch away. I hope this is a little more clear.

Outback,
How much lateral movement does the front take down lug of the upper have between the lower front ears.  Is the front of your lower/upper rock solid, or is there sideways slop.

On most of the accuwedges that I have installed, you dam near had to stand on the carry handle/upper to get the two to mate (allow the take down pin to glide threw). Unless your wedge was an aftermarket knock off, you shouldn’t be able to add a shim (even on a low shelf receiver).

The only thing that comes to mind is if the front of the your upper is loose at the front of the lower (front take down pin), then you may have gotten upper shift at trigger pull, And, when you tightened the two up more with the extra shim, this is keeping the upper from moving around at the front of the lower (not very likely, but this movement will effect a questionable scope).

On a scoped rifle, the more you can dampen the buffer impact/rifle jarring, the less likely the scope zero will be affected (focal bracket bounce).  An item that you didn't touch on is what brand of scope you are using.  On some cheaper scopes, the simple jarring of the rifle can cause the scope to change it zero point, and would explain the flyers.  

To give you an example, I have an ongoing bi-yearly battle on a Simmons scope that I bought years ago (6x18). About every six months, I have to send the scope back for replacement, due to not holding a zero.  Originally, I picked the scope up for a 22lr, but the scope found it's way onto one of my flat tops, and the ongoing replacement s of the scope has become one of my running jokes/boil on my ass, kind of things. The only reason that I still have it is that they keep replacing it for free, or I would have thrown it away years ago.

So if your scope is in question, then maybe the extra shim just slightly deadened the carrier blow/upper jumping around on the lower, and this limited dampening is just enough to prevent the scope from loosing it zero point.