I'm not an expert on humanism or Valla but I can tell you what specific errors he focuses on. Additionally you can find the Donation of Constantine and Valla's criticism of it linked here. They're rather short and translated in an accessible manner such that they're not hard to understand, but I'll bullet point the notable anachronisms that Valla examines below:

• Use of the words "diadem" and "tiara": The Donation describes the bestowal onto the pope of the "imperial diadem," described as a crown of gold, along with the "tiara," or a sort of shoulder-band around the neck. However, as Valla points out, a diadem in Roman times would have been made of cloth or silk instead of the gold crowns that medieval monarchs would wear. Moreover, the tiara was a piece that denoted eastern, usually Persian, but definitely non-Roman rulers.

We give," he says, "our imperial Lateran palace": as though it was awkward to place the gift of the palace here among the ornaments, he repeated it later where gifts are treated. "Then the diadem;" and as though those present would not know, he interprets, "that is, the crown." He did not, indeed, here add "of gold," but later, emphasizing the same statements, he says, "of purest gold and precious gems." The ignorant fellow did not know that a diadem was made of coarse cloth or perhaps of silk; whence that wise and oft-repeated remark of the king, who, they say, before he put upon his head the diadem given him, held it and considered it long and exclaimed..."And at the same time the tiara and also the shoulder-band,that is the strap that usually surrounds our imperial neck." Who ever heard "tiara" [phrygium] used in Latin? You talk like a barbarian and want it to seem to me to be a speech of Constantine's or of Lactantius'. Plautus, in the Menaechmi, applied "phrygionem" to a designer of garments; Pliny calls clothes embroidered with a needle "phrygiones" because the Phrygians invented them; but what does "phrygium" mean? You do not explain this, which is obscure; you explain what is quite clear. You say the "shoulder band" is a "strap," and you do not perceive what the strap is, for you do not visualize a leather band, which we call a strap, encircling the Caesar's neck as an ornament. [It is of leather], hence we call harness and whips "straps": but if ever gold straps are mentioned, it can only be understood as applying to gilt harness such as is put around the neck of a horse or of some other animal.

• Use of the word "satrap": This word occurs twice in the Donation referring to the nobility of Rome: "We-together with all our satraps (satrapis nostris), and the whole senate and my nobles, and also all the people subject to the government of glorious Rome...through this our imperial sanction, all the emperors our successors, and all the nobles, the satraps (satrapas) also, the most glorious senate, and all the people in the whole world, now and in all times still to come subject to our rule." Simply put, the Romans never had satraps and obviously would not have used this word to refer to members of their administration.

• References to "Byzantia": The Donation mentions the transfer of imperial power to "the province of Byzantia (in Bizantiae provinciae optimo loco)." Valla doesn't explicitly say this, but the Romans would rarely have referred to the city of Constantinople as "Byzantium" after the rule of Constantine I, nor did they ever call themselves "Byzantines," given that they never stopped being "Roman." That said, Valla correctly notes firstly that "Byzantia" would have been a city, while the actual province it was in would have been "Thrace," and that "Byzantium" was essentially the old city of Constantinople.

And how is it that he speaks of a province of "Byzantia," when it was a town, Byzantium by name? The place was by no means large enough for the erection of so great a city; for the old city of Byzantium was included within the walls of Constantinople. And this man says the [new] city is to be built on the most fitting place in it! Why does he choose to put Thrace, in which Byzantium lies, in the East, when it lies to the north? I suppose Constantine did not know the place which he had chosen for the building of the city, in what latitude it was, whether it was a town or a province, nor how large it was!

• Misdating of Roman consuls: The Donation dates itself as "Given at Rome, on the third day before the Kalends of April, Constantine Augustus consul for the fourth time, and Gallicanus consul for the fourth time (Datum Romae tertio Kalendas Aprilis, Constantino Augusto quarto consule et Gallicano quarto consule)." Outside of Valla's analysis, this would have been impossible as Constantine's 4th consulship would have been in 315 while Gallicanus's first consulship would have been in 317. Valla does criticize the idea that Constantine and Gallicanus had simultaneous 4th consulships though.

And "Constantine consul for the fourth time, and Gallicanus consul for the fourth time." Strange if each had been consul thrice, and they were colleagues in a fourth consulship!

• Conferral of "banners": The words "signa" and "banna" are used to mean "standards" and "banners" respectively in the Donation. Valla, however, points out that "banna" is a bit of a nonsense word and not at all classical. He doesn't say this, but the actual classical word for a standard would have been "vexilium," and "signa" likewise would not have had that meaning in classical times.

There are a few smaller anachronisms (ex. use of the word "seu" and the nature of the positions of consul and patrician) that you can check out in the text. It's generally a fun and brief read. As to the sources Valla would have used I cannot say exactly as I'm not an expert on humanism. Though I can generally say that Valla likely had access to the same, if not more, classical sources that we have access to today, given that the vast majority of those we do have are passed down by medieval scribes.