Brutus FYI your rifle is most likely shooting just fine, i.e. good enough for a TR shooter to win a match with it. If you want to verify that the best way to test your rifle and ammo is with a scope and rest. I can see from your photo that you have a real Target Rifle. Unless the barrel is worn out or there is something wrong with the action or bedding (and all of these can be fixed) you can reasonably expect to be able to get well under 1 MOA groups at 300-600. If you do everything right, it is even fair to be able to expect that you will be able to approach 0.5 MOA groups for 10-15 shots.
FWIW I have shot my TR (a Musgrave with a MacLennan barrel, in my case) off of bags and with iron sights on a couple of occasions. Firing at standard DCRA 300m targets, it seemed that 10 shots pretty reliably gave me groups that would produce scores of 50.7V plus or minus one V. Which I find interesting because when I am really shooting well, that's about what I am able to accomplish off my elbows. Also interesting is that I know that the rifle (I used to shoot it in F Class) is capable of 0.5 MOA groups.
manitou210, the 15 out of 15 Vs that you saw at Connaught last week, was that on a TR target or on some other target?
The DCRA TR 300 yard and 300 metre targets are pretty tight targets; the 5-ring is 1.8MOA and the V-bull is 0.9 MOA. It is *very* unusual to see a score of 50.10V being fired on this target. I don't know if I have ever seen or heard of a 75.15V being fired on this target. So if the guy you saw shooting (who was it BTW?) did this with iron sights on the 300 TR target, you really saw something special happen.