Range Officer Potential?

What is the potential precision of a stock Range Officer in .45 ACP?  Would the shots in the group normally be random or some type of pattern, i.e. vertical or horizontal strings?

Pattern? I think that would have more to do with ammo. Just my guess. As for potential? I shot a 93-3X on a practice 50 yard slow fire target yesterday with my RO in mild wind. One 6, one 8, and one 9. Groups good. The only thing I've done to it is fit a new sear, replace the mainspring with one of lighter poundage, and I cleaned up the travel of the trigger itself because it was rough and gritty. I added grip tape to front strap and target adjustable stocks. These after purchase mods are done for the shooters comfort and preference. Nothing was done about the barrel, link, pin, or bushing which - in a pure ransom rest mechanical way - that's where the accuracy of the gun comes from. The other stuff, the mods I made, were for ease and the ability to shoot it well. If you're thinking buying one I think it's the best bang for buck when you might not be able to afford a nicer or higher end gun. And the nice thing about the RO is that once you get to the point of trying to make master or high master you can have it tuned or accurized and probably still underprice the more expensive guns.

As a RO is a production gun that is not sent with a test target the results will vary and of course every gun will vary depending on your ammunition. 

FWIW... I shoot a stock RO. I have an expert classification. My best 50yd slow fire is a 96. I have put it in a ransom rest and now that I know more I know that I tightened it down wrong. Even with that, it shot under 3.5 inches. 

I can only speak for mine, but it definitely shoots a group and I am happy with it.

Of the ones I've tested, none have been worse than 3.5" with mixed brass 200gr LSWC

I would say for the price you can't get much better for an out of the box bullseye/service pistol gun. Specially if you can get some dealer pricing from an FFL. 

My personal RO which is stock except for the sear will put 10 shots in the 10 ring off a sandbag at 50 yards. If I recall 6 or 7 were x's. Thats good enough for me:)

Well, it looks like I still have work to do based on the above before upgrading my RO or getting something better.  I can barely keep it within the 9 ring at present.  Quite an accomplishment from my humble beginnings though.

-If you are really unhappy you could fit a new bushing, that is about the cheapest and most important part accuracy wise.  While I know it makes no difference, the ils-msh grinds my gears but that is also an easy swap. 
-We are lucky to have a gun this nice priced where it is.
-Do more dry fire practice.