In the Extraordinary Form of Mass, the Penitential Rite (the Confiteor) ends with the priest saying two prayers (to which we respond "Amen"). I will focus on the first of these prayers, which has been retained in the Ordinary Form:
"Misereátur vestri omnípotens Deus, et dimíssis peccátis vestris, perdúcat vos ad vitam ætérnam."In the Ordinary Form, this prayer is essentially the same:
"Misereátur nostri omnípotens Deus, et dimíssis peccátis nostris, perdúcat nos ad vitam ætérnam."The only difference is that the priest is praying for everyone present (himself included), not just for the congregation.
Now, the translation of this prayer is usually rendered as "May Almighty God have mercy on us, forgive us our sins, and lead us to everlasting life." I see it that way in English-Latin 1962 daily missals, and that's the way it is said in the English version of the Ordinary Form of the Mass. But it's not what the Latin says. A literal translation of the Latin is "May Almighty God have mercy on us and, our sins having been forgiven, lead us to eternal life."
It might sound clunky, but that's what it says! The word "dimissis" is a perfect passive participle in the third person plural ("they" referring to "our sins"); on the other hand, "Misereatur" is a present passive subjunctive in the second person singular ("You" referring to "Almighty God").
If the Latin were to mean "forgive us our sins", it would have to be dimittas peccata nostra instead, which matches the model of the first part of the prayer. (The verb dimittas (active voice) might be wrong; it might be properly dimittatur (passive voice), but I don't know whether the verb should be in the active or passive voice here. It seems that misereatur is in the passive because it is a conjugation of misereri -- not miserere -- which is a deponent verb, which means it looks passive but is translated as active. I don't think dimittere is deponent, so the active voice seems more likely to me to be correct.)
The new English translation of the Order of Mass (for the Ordinary Form) gets it right.