I'm a new homeowner with plenty of theoretical background in electrical engineering but until now, zero practical experience in home wiring. I recently replaced a few 2-prong outlets with 3-prong outlets and GFCIs. I plugged in my receptacle tester, and the rightmost two lights illuminated, showing a reading of Correct. When I press the Test button on the GFCI or receptacle tester, the outlet goes dead, and turns back on when pressing Reset. Is that reading of Correct all I really need to know to tell me that I did the job correctly? It's my understanding that there are ways to "fool" a receptacle tester to give a Correct reading even though the wiring isn't actually correct.
Are there any common pitfalls that would cause a Correct reading despite incorrect wiring? Or does that usually result from deliberate miswiring that would be unlikely to do by accident? I'm reasonably confident I did the job correctly, but am wondering if the receptacle tester output can give a false sense of security.