I have a shower downstairs where a 6" shower arm comes out of a wall that was connected to a 90 degree threaded joint inside the wall. My roommate without my permission took out the 6" arm and installed an 'S' arm. She did a poor job (did not take out the old thread/puddy, didn't put in new pipe thread, didn't caulk the metal circle that covers the hole in the wall). Although the concept is simple, a leaky threaded joint in the wall will cause a lot of damage, and is unnoticable until its too late. I took the 'S' arm out, got a new 6" arm, tried my best to take out old tape (the hole in the wall is only 1.5" by 1"), wrapped the pipe thread 3~4 times on the arm thread going into the wall, HAND tightened the arm, and checked for leaks on the threaded joint with the water on WITHOUT a shower head on. Caulked the donut plate with silicone caulk.

My regrets:
I read installation of arms online, and it says to use a pipe wrench to tighten. I only used my hand. Although it was really tight according to my hand, I don't know if I could have done another rotation with a wrench to make it better

I didn't put the shower head on the pipe when checking for leaks. The water was just free flowing like a hose so I don't think it was a good test of the threaded joint. Should I have capped the arm and then checked the joint? The metal donut is on now, so I can't see into the wall.

When putting weight on the arm, I notice the silicone caulk in the hole of the metal donut flexes with the arm slightly. Maybe up to a mm. Should I have used a caulk that dries hard to keep the arm firm?

I'm afraid of leakage I can't see in the wall, and a plumber would cost $75 to $85. What should I do to install this arm right? Since a plumber will undo what I did anyway, I'd like to try again.

Since there isn't much back pressure from the shower head hand tightening the shower arm ought to be fine. You don't put a pipe wrench on chrome. If you want to snug up the shower arm pull the chrome escutcheon plate,(metal donut) down and snug up the arm with a pair of pliers. That way any nicks and scratches will be hidden. The shower arm is secured by two screws in the drop eared ell.(see image) and that is what keeps the shower arm tight not the caulking. I guess that you could pull the escutcheon plate down on the arm and turn the shower onto check it for leaks but we have very few shower arm leaks. Good luck, Tom

For the benefit of others that may stumble upon this page (as I did) while searching for info on shower plumbing, please note that newer low-flow and ultra-low flow shower heads DO create quite a bit of back pressure and may cause leaking where a normal-flow shower head would not (or had not before).
Even when tightened with something more than your hands, shower arms can leak inside the wall if the threads on either the arm or the ell are imperfect and insufficient thread sealing methods are used. My recent shower installation (using all new components) required 12 turns of standard duty teflon tape on the shower arm threads and significantly more than hand tightening to achieve a watertight seal.
And speaking of more than hand tightening, if you have a low-profile escutcheon (the decorative plate that covers the hole in the wall where the shower arm protrudes), it may not cover enough of the shower arm to hide any scratches left from tightening it with a wrench/pliers. In these cases, simply slip something sturdy of an appropriate diameter INSIDE the shower arm and use the extra leverage to fully tighten the arm - I recommend something other than a screwdriver; its small diameter shaft can concentrate the force applied in a small area and possibly distort the shower arm.
As the original poster noted; a leaky threaded joint in the wall can cause a lot of damage, and will most likely go unnoticed until it's too late.