It is my understanding that the reason God needed to deliver a
teaching to Mohammed in the first place is because the Jews and
Christians irredeemably strayed from the teachings of Moses and Jesus.
I understand that the Quran talks many times about children of Israel, but not all the time, neither half. I do not know in what reasoning the "first place" part is based on.
(...) Christians irredeemably strayed from the teachings of Moses and Jesus.
I think that assumption is wrong since irredeemably strayed is something like away from God, and near the evil, this kind of (anti-)followers are presented in all forms in all ethnic groups.
The Jews strayed from Moses The Jews strayed from Jesus The Christians
strayed from Jesus
Continuing I think its hard to know what versicle was targeting what specific "ethnic" religious group or if (God) intended to target one at all (this implies discriminating other groups). Since praying, fasting, believing in One God, believing that something else is a deity can applies to ethnic and non-ethnic muslims, christians, jews, etc. Any of them can be strayed from the messengers of God (Jesus, Moses, etc.).
The Quran even talks about people that usually lived in forests that didn't believe in one God, most of all are extinguish, so I can even ask the same question regarding only the people that lived in the forests. (26:176)
It's a matter of authenticity and making your path more easy. The reason God, gives a proof in Arabic that has no contradictions and its a miracle in its reasoning form, if we can consider "reasoning" science. Assuming that the main target was the Jews or Christians its wrong because its referenced that its a message for all humanity. (12:104) So God did discriminate no group when He teached the messenger.
Does Islam have an opinion on approximately when
Christians have a central foundation that it is in Vatican, Islam doesn't have that kind of central foundation that potentially give an opinion. But I'm answering the answer as Christian (follower of the Book).
Islam means Submission to God, in that context my direct answer is no, since its a matter of opinion, and I think God is the One that can give you the answer that would be more than a opinion, but a answer full of truth and science.
Everyone of the Jewish, Islamics, Muslims, etc, will be rewarded according to their doings as it is in this versicle (2:62). So even if you think that the bad example from the Quran, is from a ethnic jew, arab, or christian, or you interpret in that way, all of them must follow the good example, not only the jews or christians. (2:148)
When did the Jews/Christians go wrong?
In my view:
The Jews go wrong if they forget God. When they do sins. Do not follow its own book. (Torah as good reference - It's referenced in the Quran)
The Christians: When they forget God. When they do sins. When they do not follow the Salms and the Envagelho (Jesus), referenced in the Quran too.
To any of both groups that recieved the Quran revelation:: When they forget God. When they do sins. When they forget to following the Quran (or the previous Books, if they are sacred - referenced in the Quran, such as the Torah, Salms).
So in the Quran (and the Torah) you find many examples that applies to every group, and not a specific one. (I'll assume for example that forgetting God is the main one).