Are there other ways in which 60Hz noise can get into your system?
Yeah lot's of ways. 
Besides those already listed... 

If there is a cylindrical inductor in the circuit.  (loops can be other than in just the ground line.)

Room lights sometimes.. though more often this is capacitive coupling from florescent lights and at ~20-50kHz. 

Vibration (usually at 120 not 60Hz... I assume harmonics are included.)

The best way to check is to move your circuit around.  And see what happens.
Things get worse as you move toward the source,
inductive things will have an orientation dependence. 
you can block electrostatic things.  

At the ridiculously low sub microvolt level, I've seen capacitve coupling between wires carrying power to different circuit fragments.  (Though this was not 60Hz.)