A new ruling given by Rav Yonatan Raziel states that it is forbidden to correct a mistake made in the public Torah reading.
Rav Raziel cites a question posed to Rav Nachum Rabinovich, Rosh Yeshiva of the Hesder Yeshiva in Maale Adumim (Birkat Moshe), where he rules that while reading the Torah correctly is a Rabbinic law, the law against embarrassing the reader is a (written) Torah law and takes precedence.
While, of course, Rabbi Raziel stresses that in an ideal situation you will also have the correct reading, in the event of a mistake, not embarrassing the reader should be the priority.
He also says that, in any event, individuals from the congregation should not shout out at the reader, rather one gabbai should be appointed to be responsible. He also warns to be particularly sensitive with younger readers, who may be more sensitive than older readers.
In the words of Rav Rabinovich, expressing his support for Rav Raziel’s ruling, he says “it is better that the congregation not fulfill their obligation of reading, rather than transgress the sin of embarrassing a person.”