Strange noise coming from my bathroon outlet
Yes this is indicating a problem. It's hard to tell what the issue might be, but electricity is silent when its working right. 

BEFORE INVESTIGATING - turn off the breaker.

Things I would check AFTER turning off the breaker:


take off the outlet cover and look for

burn marks
loose wires
cracked or worn insulation
cracked or worn parts on the outlet
signs of rodents

take off the switch cover and look for the same things as the socket


The easy try-it-and-see repair is to replace the switch and outlet, this should cost maybe $10 and 30 minutes of work.

Do you know if you have aluminum or copper wiring in your home?

Is there a fan in this bathroom? Are you sure the noise was coming from the outlet and not a breeze blowing past the fan?