If you forgot to add a critical insert in the 'Amidah (one of the special additions to Shemoneh 'Esreh at certain times of the year, eg., HaMelech HaKadosh, Ya'aleh VeYavo, etc.), and you realize at the next service that you definitely forgot to say it earlier (eg., you got the date wrong and someone pointed it out to you, or you forgot the next time also but you heard the Sha"Tz say it), do you need to make up for it (Tashlumin, perhaps because it is as if your earlier prayer did not happen), or is Tashlumin not warranted (perhaps because it was a flawed, but fulfilled, prayer)?
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The sefer "Shegiyos Mi Yavin" (a compilation of the laws of mistakes in davening and brochos) writes (Chapter 14 Seif 4) - my own translation:
Essentially, yes you should still pray Tashlumin if you would have had to go back and pray at the time.
However, this is only true if you would make up for your mistake. However, if you forget Yaaleh veYavo at Mincha on the last day of Rosh Chodesh then saying two Maarivs wouldn't solve anything because you don't make up the missed Yaaleh veYavo. You can still pray a second time as a Nedava if you want (assuming it isn't Shabbat or Yom Tov).
However, this is only true if the thing you skipped was not essential to Shmoneh Esrei (ie do we consider your earlier prayer a messed up prayer or a non-prayer?). If it was essential, then it is as if you didn't pray and you have to pray Tashlumin just like regular. Examples of things which are essential include Shabbat and Yom Tov according to one opinion in Tosfot (though we rule it is a doubt and one should pray Tashlumin as a Nedava if possible).
Source for the above: Shulchan Aruch OC 108:11 and Mishna Berura there
Additionally, Rabbi Chaim Soloveichik of Brisk in Chiddushei HaGrach al haShas II (Stencils) page 36 writes that Tal uMatar is considered essential while Yaaleh veYavo is not.
According to what I learned, you would not need to do Tashlumim if you realized at the next service that you have missed a critical insert.