The best answers for this sort of question are found in the literature and via discussions with colleagues. Decisions about such things are matters of science, not technical support. In many cases there is an active literature specifically addressing the concern. For instance, for electrodermal activity (skin conductance):
Van Doren, M., de Vries, J.J.G., and Janssen, J.H. (2012). “Emotional Sweating Across the Body: Comparing 16 Different Skin Conductance Measurement Locations”, Physiology & Behavior, 106:298-304.
Another case that is still widely debated is the positioning of electrodes for impedance cardiography. Many different types and geometries of electrode have been used. The guiding theory behind all of them is that the electrical impedance through the thoracic cavity should be modulated by the amount of blood providing a path for currents to flow through that cavity. To measure this impedance, a small current is injected through the body. To inject this current, two electrodes or sets of electrodes are connected to the subject, one on the neck and the other on the abdomen. The actual measurement is of the change in voltage along the path of the current. Thus a second pair of electrodes or sets of electrodes are attached interior to the first pair. That is, one electrode below the upper current injecting electrode and another above the lower current injecting electrode. For additional information, see references in “What types of electrode should I use?”
In other cases, the science is much better established. For determination of heart rate with ECG electrodes, the primary concern should be to record an R-wave that is large compared to all other ECG components. Measurements of electrical potential differences along the axis of the heart, which is generally oriented (in humans) from the subject’s upper right to lower left chest, best accomplish this goal. Willem Einthoven was awarded a Nobel prize in 1924 for his work in characterizing the electrical activity measurable on the skin surface as a result of processes occurring in the heart. As a means for merely detecting heart beats, this is no longer an area of active science.
Although the relevant electrical signals were considered tiny in the 19th and early 20th centuries, by modern standards the ECG signal is large and generally easy to measure. It can be obtained with electrodes at almost any location on the body.1 Best results, though, will be obtained with both measuring electrodes placed at locations relatively devoid of underlying muscle, one on the subject’s lower left (typically on a rib or on the left ankle) and the other at the upper right (typically just under the clavicle or on the right wrist). Based on Einthoven’s terminology, this configuration is referred to as LEAD II. The general standard is to measure the voltage drop from the lower left to the upper right as the heart depolarizes, so the positive electrode (VIn+, usually indicated with a red lead wire) should be at the lower left while the negative electrode (VIn-, usually indicated with a white lead wire) should be at the upper right.
In all cases of electrode placement, the criteria that make some locations better than others relate to the anatomy and physiology of the subjects, the logistics of the experiment, and concerns about subject comfort. A desire to avoid movement artifacts suggests that electrodes are better placed on the chest than on the limbs, but limb locations are generally more easily accessible and introduce fewer concerns about subject privacy.
Some environments may introduce particular difficulties. For instance, in an MRI scanner, the LEAD II electrode configuration is generally not the best. Please note that the static magnetic field changes the ECG signal. It does not just introduce “noise” but literally changes the electrical potentials at the skin surface because of its effects on the charged particles that produce and carry the signal. The radio frequency magnetic field variations generated by active scanning, however, do introduce noise that may easily overwhelm the ECG signal. In the scanner, arraying the electrodes along or perpendicular to the bore of the magnet is a better strategy than a standard LEAD II configuration. For more, see:
Niendorf, T., Winter, L., and Frauenrath, T. (2012). Electrocardiogram in an MRI Environment: Clinical Needs, Practical Considerations, Safety Implications, Technical Solutions and Future Directions, in: Millis, R.M., Ed., Advances in Electrocardiograms – Methods and Analysis, chapter 17, pp. 309-324.
Ranogajec, S. and Geršak, G. (2014). Measuring site dependency when measuring skin conductance, 23rd International Electrotechnical and Computer Science Conference ERK.
Tsiamyrtzis, P., Dcosta, M., Shastri, D., Prasad, E., and Pavlidis, I.T. (2016). Delineating the Operational Envelope of Mobile and Conventional EDA Sensing on Key Body Locations, Proceedings of the 2016 CHI Conference on Human Factors in Computing Systems:5665-5674.
For the case of electromyography (EMG), there are published guidelines created with the intent of standardizing procedures and/or particular placements. Useful information may be found, for example, in:
Fridland, A.J., and Cacioppo, J.T. (1986). “Guidelines for Human Electromyographic Research”, Psychophysiology, 23(5):567-589.
Hermens, H.J., Freriks, B., Disselhorst-Klug, C., and Rau, G. (2000). “Development of Recommendations for SEMG Sensors and Sensor Placement Procedures”, Journal of Electromyography and Kinesiology, 10(5):361-374.
Stegeman, D.F., Hermens, H.J. (2007). “Standards for Surface Electromyography: The European Project ‘Surface EMG for Non-Invasive Assessment of Muscles (SENIAM)’.”, 108-112.
and for the specific case of facial EMG:
van Boxtel, A. (2010). “Facial EMG as a Tool for Inferring Affective States”, Proceedings of Measuring Behavior 2010 (Eindhoven, The Netherlands, August 24-27, 2010), Spink, A.J., Grieco, F., Krips, O.E., Loijens, L.W. S., Nodlus, L.P.J.J., and Zimmerman, P.H., Eds.
and for the specific case of startle eyeblink reflex:
Blumenthal, T.D., Cuthbert, B.N., Filion, D.L., Hackley, S., Lipp, O.V., and van Boxtel, A. (2005). “Committee Report: Guidelines for Human Startle Eyeblink Electromyographic Studies”, Psychophysiology, 42:1-15.
1 Clinical considerations notwithstanding, BIOPAC products should never be used for diagnosis or treatment, but it should be pointed out that positioning of electrodes requires greater care under some circumstances. See:
Kligfield et al. (2007). “Recommendations for the Standardization and Interpretation of the Electrocardiogram Part I: The Electrocardiogram and Its Technology: A Scientific Statement From the American Heart Association Electrocardiography and Arrhythmias Committee, Council on Clinical Cardiology; the American College of Cardiology Foundation; and the Heart Rhythm Society Endorsed by the International Society for Computerized Electrocardiology, 115:1306-1324.