The Milgram experiment was conducted by Stanley Milgram, and it measured the obedience that people display towards authority figures. In these experiments, participants were asked to obey an authority figure who asked them to administer shocks to a patient. The shocks were not real, but the participants were not aware of this.
There are several ethical dilemmas here, with the most important one being the trauma that the experiment might have caused on participants. The experiment showed many people that they were actually capable of committing terrible atrocities just to follow orders. This was a realization that had a significant impact on people.
Although no one was physically shocked, many people believed that the subjects were, and this was a source of stress and worry for participants. Moreover, this also means that the participants were not told all the details of the experiment, which some critics find unethical. I do not think that the ends always justify the means, and I think this situation presented some serious ethical problems. If a replication of the experiment actually shocked people, the ethical problems would increase.
The experiment found that a very high percentage of people were willing to compromise their ethical values in order to fulfill the orders of others, even when this caused pain to the subjects.