Simply removing line frequency noise with a notch filter can have adverse affects on the signal. For example, a deep notch filter will often an impulse response that rings. Without knowing the amount of ringing, how close other signals are to the line frequency, one may design a filter that causes other system problems. The deeper and narrower the notch, the more ringing is likely to be an issue.
As an example for removing line-frequency noise from ECG signals, 60601-2-25 and -2-27 both require testing with a 3 mV, 100 ms pulse and verify that the overshoot and return to baseline are within limits. (See medteq link).
If there is any chance this product will need to operation in a country with 50 Hz line frequency, it is a good idea to support both 50 and 60 Hz line frequencies
If you truly want to remove only the line frequency signal, then using an adaptive noise cancellation such as suggested by David Mortara is a well used solution and reliable solution. See Mortara, D. W. 1977. Digital filters for ECG signals. Computers in Cardiology, 511–14.