Did Frankenstein overstep certain ethical boundaries as a scientist? Why or why not? Can you think of any real world examples where scientist take part in questionable research or experiments?

From a Christian perspective, which would have been the predominant perspective when the book was published in the nineteenth century, Frankenstein crosses an ethical boundary when he creates life. This was considered unethical because it defied God. Creating life was the privilege of God, not man.
In a broader sense, Frankenstein also acts unethically when he robs graves for recently deceased bodies, obviously without having any permission to do so. He also doesn't seem to give very much consideration to the wider implications of his experiments, and abandons responsibility for those implications when he abandons the creature.
As for real world examples of unethical scientific experiments and research, there are plenty of cases to choose from. In Nazi Germany, for example, experiments were carried out on concentration camp prisoners. At Ravensbrück, for instance, bones, muscles and nerves were removed from prisoners (without the use of any anesthesia) in order to study regeneration.
Another, more recent example of unethical science is the CIA-funded Project MKUltra. From 1953 to 1973, American and Canadian citizens were, without their prior knowledge or consent, given various psychotropic drugs and subjected to various forms of sensory deprivation and torture. The victims of these experiments were often from hospitals or prisons, and the CIA hoped to use these experiments to create mind-controlling chemicals that they could use against the Soviet Union.