The receptacle testers are very useful. I have a bunch of them so I can usually find one when I need it. I buy the ones with the ground fault circuit interrupter device test button on them.
There is one limitation to these testers which is the inability to detect what some people refer to as reversed hot and neutral, with a "bootleg ground". This is a condition I have encountered more than once in homes where the homeowner, or clueless handyman has reversed the hot and neutral wires, and also connected the receptacle equipment grounding terminal to the incorrectly connected neutral wire.
Here is a website with a diagram that illustrates it better than my written description: Failures in Outlet Testing Exposed which also shows a more reliable way to test for this fault using a quality medium sensitivity non-contact voltage detector on the grounding terminal of a receptacle. Very well written article.
One way to test for wiring errors in receptacles on different circuits that are some distance apart is to connect a three wire extension cord into one receptacle, and use an AC voltmeter at the other receptacle to see if any substantial voltage, (more than maybe 6 VAC) exists when putting the meter leads between the two grounding lugs. Likewise the neutrals should not have much difference. And a meter reading between neutral and ground should not show much voltage between them. You might see a difference of a few, or as much as 240 VAC measured between the two hots, depending on which phase of the power it is connected to in the panel.
If you see something like thirty or forty volts between grounds or neutrals even if you don't burn something up or get a shock, you might have problems with 60 Hz noise. If you do this test with a load like a lamp plugged into one or both circuits and you see a big difference, don't connect any of your equipment to either circuit until the fault is rectified.
I am not a licensed electrician, but I have independently studied the coursework that my local community college uses to train electricians. And I have been an electronics technician, and field service engineer in very high-tech and industrial environments for over forty years. Anyone who knows me, calls me whenever they need electrical work. And I have installed numerous service entrances and done residential, and commercial electrical work with permits and inspections, and have never failed an inspection.
I started taking photos of very dangerous electrical installations that I have found, and some of them are shocking! Pun intended. I have found wiring blunders that were like a trap waiting to kill someone. I quit photographing them because there were so many of them. I have found poor workmanship resulting in installations that were actually smoldering, and likely within hours of starting a fire in someone's home on two occasions. One the result of improper repair work on aluminum wiring, and another involving a loose connection resulting in heat buildup due to unintentional resistance at the connection point to the wiring device.
It is amazing how much unsafe wiring is out there.