Common mode rejection can be a great challenge, if you only rely on the InstrumentAmp. Often RF can be converted from a CM noise into a differential signal since it is beyond the BW where CMRR is useful, so RF suppression methods must be used such as ferrite Baluns and RF cap.
The other most common noise is galvanic skin response of the electrode interface where skin chemistry with electrodes creates a natural battery voltage modulated by motion, thus selection of materials must follow the best practises.
As with any signal conditioner, the optimum channel filter matches the signal spectrum, which must be well understood to reject noise to gain the highest SNR. In addition, deep notch AC filters are often included to reduce any residual differential hum from the large CM Electric field of AC line noise in a high impedance input.
Shielding, Filtering and CM rejection with single point floating ground reference leads and isoating digital noise from the analog are the challenge to measuring high impedance signals.
Any SMPS used for DC power will be a great source of interference including stray capacitive coupling of AC modulated RF switching noise in the SMPS. So isolation of DC CM noise is a huge requirement.