I thought it would be useful to assemble in one place the passages where Jerome comments on the Greek and Latin texts of the New Testament. The list is not exhaustive (but feel free to note additional passages in the comments). Translations are from NPNF.
In Epistle 27.1 “To Marcella”:
the Latin manuscripts of the Scriptures are proved to be faulty by the variations which all of them exhibit, and my object has been to restore them to the form of the Greek original, from which my detractors do not deny that they have been translated. If they dislike water drawn from the clear spring, let them drink of the muddy streamlet …
Later in the same epistle (27.3), Jerome criticizes four specific Old Latin readings:
They may say if they will, “rejoicing in hope; serving the time,” but we will say “rejoicing in hope; serving the Lord” (Rom 12:11, 12).
They may see fit to receive an accusation against a presbyter unconditionally; but we will say in the words of Scripture, “Against an elder receive not an accusation, but before two or three witnesses. Them that sin rebuke before all” (1 Tim 5:19, 20).
They may choose to read, “It is a man’s saying, and worthy of all acceptation;” we are content to err with the Greeks, that is to say with the apostle himself, who spoke Greek. Our version, therefore, is, it is “a faithful saying, and worthy of all acceptation” (1 Tim 1:15).
Lastly, let them take as much pleasure as they please in their Gallican “geldings;” we will be satisfied with the simple “ass” of Zechariah (Matt 21:2–5).
In Epistle 71.5 “To Lucinius”:
The new testament I have restored to the authoritative form of the Greek original. For as the true text of the old testament can only be tested by a reference to the Hebrew, so the true text of the new requires for its decision an appeal to the Greek.
In The Perpetual Virginity of Blessed Mary, against Helvidius:
And yet you with marvellous effrontery contend that the reading of the Greek manuscripts is corrupt, although it is that which nearly all the Greek writers have left us in their books, and not only so, but several of the Latin writers have taken the words the same way. (8)
Seeing that you have been foolish enough to persuade yourself that the Greek manuscripts are corrupt, you will perhaps plead the diversity of readings (18)
In Against Jovinian:
The Latin words do not convey the meaning of the Greek. What words shall we use to render Πρὸς τὸ εὔσχημον κὰι εὐπρόσεδρον τῷ Κυρίῳ ἀπερισπάστως? The difficulty of translation accounts for the fact that the clause is completely wanting in Latin manuscripts. (1.13)
… let him add what is found in the Greek copies (1.26)
The bishop, then, must be without reproach, so that he is the slave of no vice: “the husband of one wife,” that is, in the past, not in the present; “sober,” or better, as it is in the Greek, “vigilant,” that is νηφάλεον (1.35)
“… think according to chastity” (not soberly as the Latin versions badly render), but “think,” he says, “according to chastity,” for the Greek words are ἐις τὸ σωφρονεῖν … (1.37)
Preface to the four gospels:
You urge me to revise the old Latin version, and, as it were, to sit in judgment on the copies of the Scriptures which are now scattered throughout the whole world; and, inasmuch as they differ from one another, you would have me decide which of them agree with the Greek original.
If, on the other hand, we are to glean the truth from a comparison of many, why not go back to the original Greek and correct the mistakes introduced by inaccurate translators, and the blundering alterations of confident but ignorant critics, and, further, all that has been inserted or changed by copyists more asleep than awake?