This is a very valid questions and one I hear often. Women who have had to take some type of medication during their pregnancy are often worried if they'll be getting the dosage again if they ingest their placenta. This has lead me to research this area, and I'd like to share my findings.
The placenta acts as a filter for toxins, keeping potentially harmful substances from the baby. The placenta does not typically store the toxins. The toxins the placenta filters are sent back through the mother's bloodstream to be removed by the body's mechanisms.
This is good news for mothers considering encapsulating their placentas for consumption. Medications taken during pregnancy and any other toxins exposed to the placenta do not remain indefinitely in the placenta.
One thing that can be stored in the placenta is heavy metals, just the same as heavy metals are stored in our own bodies, which is what makes them so detrimental to health. Most people are not exposed to heavy metals in such a degree that I would consider the risk of having some heavy metals in the placenta to outweigh the benefits of ingesting the placenta after delivery. However, mothers who smoked during their pregnancies will have exposed themselves to more heavy metals than the average woman, and in these circumstances, ingesting the placenta may not be appropriate.