I just installed a pull chain fixture in a closet. The light works but I paid no attention to black wire to brass screw or white wire to silver. Of course when I am tossing the box I see the instructions written on the interior. Do I have to take it apart and check. Is it a potential problem?
Yes, you should fix it. If nothing else, if you crossed the wires, the threads of the socket would be hot, even with the switch off. This would give a good chance of shock when changing the bulb if you’re not careful.
Yes, it's essential because you could have wired the fixture as a switched neutral instead of a switched hot... This is deadly! Turning the fixture "off" would not truly switch the hot conductor off and you could get electrocuted with the switch in the "off" position.