Check the PH of the well water.

"Should I be concerned about other pipes behind sheetrock?"

Yes.

Since you'll be cutting/replacing this section anyway, I would suggest cutting/replacing the longest section possible at this location. Once repaired (this is not a big deal, by the way -- cheap/easy) then examine the the section you've cut out....maybe even have it cut lengthwise so you can inspect the walls throughout. I suspect you'll find evidence of deterioration all along the length. Whatever you find is what's going on throughout your system....and is something you'll want to know asap.

Certainly the pinhole could be a once-only anomaly unrelated to other stuff in the rest of your plumbing.....but I doubt it....and I'll bet you do, too.

Otherwise, agree with justalurker about checking PH.

My first question would be are you certain that you actually have a leak?

You were alerted to the problem by a small puddle of water on the floor under a vertical riser and you stated that you found a leak on the riser, but are you absolutely certain it is a leak or did you perhaps find a couple drops on the pipe near the bottom fitting and assume a leak?

Far too often homeowners find droplets of water clinging to the underside of a horizontal copper line, or near the bottom fitting of a vertical riser and automatically assume the problem to be a pinhole when it is far more likely that the water droplets on the pipe are resulting from moisture in the atmosphere condensating on the exterior wall of a pipe, and in the case of a vertical riser that condensate may be occuring on the full length of the pipe, then flowing down the pipe in a light film that is almost invisible to the naked eye until it hits the ridge on the fitting at the bottom and forms a droplet before dripping off to the floor.

If the problem is occuring as a result of condensation you can eliminate the problem by insultating the line, however if you are certain that you actually have a pinhole leak, the only real solution is to replace the line.

Normally pinholes will show up first on horizontal lines and a true pinhole will manifest itself with a microfine mist spray.

If you determine it is a pinhole and you opt to replace the line you may want to consider replacing it with CPVC or PEX.

Lazypup: I can actually see the pinhole. And it is a horizontal run. I don't think that it is condensation, as it is 62 degrees in the basement, and we normally get condensation in the summer.

I like your idea of replacing with PEX. I've been looking for an "excuse" to buy PEX tools, and was leery about PEX leaking and copper being superior in that regard, but not anymore...

Thanks to the others who replied, also.

Before you jump out there and buy PEX tools consider this...although the PEX tubing is impervious to the acids that cause pinholes, all the PEX enduse fittings are made with the same grade of copper as you have now, and they are just as likely to incure pinholes.

On the one hand you could switch to CPVC, which is impervious to the acids but,

On the other hand, if there is anything in your water that is detrimental to the pipe, what is it doing to your body? For personal health reasons, I would be more inclined to identify the problem and consider a water treatment system instead of a type of pipe that is more tolerant of the problem.

You have well water that is hard so you already know your water is problematic. The same water conditions that are attacking your plumbing are acting on all your fixtures and appliances.

Unless you want to embark on a never ending crusade of repairing pin hole leaks in the most inaccessible pipes in your home, when the leak finally becomes apparent, identify the cause and cure that.

Before you run out and spend money on PEX tools get a comprehensive water test from an independent lab. With those test results we can advise what needs to be treated and how.

"Note: I have well water, and the water is "hard". Would this cause corrosion?"

It depends on what is in the water.

A good lab test will break everything down and not just report 'hardness' numbers.
pH is not the only ting that can result in copper damage.

Fix the problem before you attack the symptom of the problem.

If you determine that the pinholes in your copper pipes have been caused by a ph of 6.2 and you have corrected the problem with a neutralizer; must all of the pipes now be replaced, or will the neutralizer stop the corrosion in its tracks and prevent future pinholes?

I just ran pex and used the plastic fittings that go with it. I used Uponor and I bought the Milwaukee expander for it. Be aware of the reduced diameter of the pexand the fittings. This creates a bushing effect and leads to reduced water pressure. My advise is to put a Pex fitting and a copper fitting in you hand and compare to see what I mean. I would use pex if I was you.