For an easier way to spin-test arrows you can roll them across any flat, smooth surface, such as a coffee table, that is short enough to allow the point and fletching to hang off the end. Just roll the arrows and see if there is any wobble in the point or nock end.
If both wobble it's probably an inferior arrow (not stright). If only the broadhead wobbles then it's not in proper alignment with the shaft. You can try different remedies to get them right. Sometimes a rubber O-ring can help. Or a nylon washer made for this. Try different heads on different arrows. Remember, you only have to get a couple right. You don't need the whole dozen.

I did notice from your signature that you are shooting 350's. These are probably a little sitff for your setup, but really shouldn't havge that much effect on grouping ability. I shoot GT Pro 22's, with a .300 spine as low as 52# with very good results, and these I could shoot at about 75#. Just goes to show that stiffer is better (wish my wife would say that).

The other guys have mentioned it may be form related. It's true, and probably grip. Over on www.bowsite.com there is a good tutorial about how to properly grip (NOT) a bow. Look under "features/practical_bowhunter/get a grip. It has pictures and all and is by far a lot easier than trying to explain it all.
Shooting an open hand is not good either. To hold your hand open involved tightening muscles in the hand and forearm, which should be as totally relaxed as possible. And many people have a tendency to start grabbing the bow upon release if they shoot an open hand. Read what I told ya about GRIP.