There are multiple explanation in Chazal as to what the mekalal did wrong: According to one view he rejected the idea of lechem hapanim being left out for a week; according to another view is could not tolerate not receiving a spot in the camp just because on his father's side he was related to a Mitzri and not part of any sheivet. Whatever the case may be, the mekalel blasphemized G-d's name and was guilty. He was held in prison until Hashem clarified to Moshe that he deserved the death penalty, after which the Torah tells us that Bnei Yisrael stoned him. The Torah then adds an enigmatic concluding sentence to Parshas Emor: "U'Bnei Yisrael asu ka'asher tzivah Hashem es Moshe," that Bnei Yisrael did what Hashem commanded to Moshe (24:23). The pasuk already told us that the mekalel was judged and executed -- what does the Torah add with this concluding line?
A number of answers are given by the classical meforshim. Rashi explains that not only was the execution carried out, but all the associated halachos involved in the process were fulfilled as well. Ibn Ezra writes that this concluding statement refers back to the other halachos given in the parsha, e.g. the laws of damages. Not only was the mekalel killed, but these halachos too were accepted and fulfilled. Ramban reads the pasuk as addressing the morality of Bnei Yisrael's actions: The execution was carried out only to fulfill G-d's command, "ka'asher tzivah Hashem," without malice or desire for vengence.
Abarbanel has a unique reading of the parsha that sheds a bit of a different light on this pasuk. The mekalel was the son of a Jewish mother and an Egyptian father. This mixed lineage left Bnei Yisrael unsure of how to treat him -- should Torah law be applied equally to this half-member of Klal Yisrael? Was the mekalel fully Jewish and subject to the same halachos as everyone else? (Abarbanel does not get involved in the technical details of whether the child had geirus or not -- see Ramban who discusses.) The "hava amina" of Bnei Yisrael was that this case was different, and the "yichus" of the mekalel to his father the Mitzri was grounds for an exemption from the death penalty.
Moshe Rabeinu decided to investigate further and ascertain whether the whole story of this mixed lineage was correct. He put the question directly to the mekalel's mother: Who is the father of your child? It's a fascinating catch-22: If the mother defends herself and claims the father is Jewish, her son wouldn't have a leg to stand on in terms of avoiding the death penalty. If the mother says the father is not Jewish to get her son off, she blackens her own reputation by admitting to znus with a Mitzri. While Rashi interprets the mekalel's mother's name, Shlomit bas Divri, in a pejorative light -- she called "Shlomit" because she used to say "shalom" to everyone she met; she was called "Divri" from the root d-b-r because she had no constraints in who she spoke with -- Abarbanel interprets the same name in a positive light. She was called "Shlomit" because she wanted to be "mashlim" her son and protect him; she was called "Divri" because she was not afraid to speak out on his behalf, even at the cost of sullying her own reputation.
The Torah ends the parsha by telling us that Bnei Yisrael carried out the death penalty, "ka'asher tzivah Hashem..." Even though Bnei Yisrael held m'sevara that an individual of Mitzri descent should not be put to death, even though in their hearts they thought the law should be different, they nonetheless carried out the sentence as instructed.
In some sense, the behavior of Bnei Yisrael serves as foil to the mekalel himself. The mekalal could not understand the law of lechel hapanim or could not accept the judgment against him in terms of nachala, and therefore rejected Torah. Bnei Yisrael's thought the mekalel should not be subject to the death penalty, but carried out his sentence despite their reservations.
The Abarbanel's introduction of Bnei Yisrael conflicted attitude toward the mekalel sets the stage for the interpretation of the Radomsker. While Abarbanel frames the doubts of Bnei Yisrael as a legal issue -- should an individual with a Mitzri father suffer the same death penalty as a full Jew -- the Radomsker frames the issue as a psychological one. "Vayinatzu bamachaneh," writes the Radomsker, does not simply mean the mekalel's dispute took place in public view -- it means the public itself was torn by the issue. Where there once was complete commitment to Toras Moshe, there was now in the eye of the public two views -- the view of Moshe, and the view of the mekalel -- that stood in conflict. What once would not have even been given a passing thought was now deemed a view that one must at least contend with, even if ultimately rejected.
The idea of "u'bi'arta ha'ra m'kirbecha," is not simply about meting out punishment to wrongdoers. It's about fixing "kirbecha," what's inside of you. It's about uprooting the wrong ideas that take hold after exposure to the mekalel or whatever the outside influence is. "U'Bnei Yisrael asu ka'asher tzivah Hashem es Moshe" -- once the mekalel and his corrupting influence was removed, once the seeds of doubt and / or psychological confusion were removed, Bnei Yisrael returned to their original level of commitment.