I started Niels Peter Lemche's Prelude to Israel's Past. I have two items:
1. The first item concerns anachronisms in the Hebrew Bible. Genesis 11:31 says that Abraham came from "Ur of the Chaldeans", which is not an accurate description of the time of Abraham, since the Chaldeans did not live in Ur until the eighth century B.C.E. But Lemche does not regard that as an anachronism that makes the entire Abraham story have a first millennium date, for he says that a later copyist could have added "of the Chaldeans".
But Lemche still thinks that the Genesis and Exodus stories reflect the first millennium B.C.E. rather than the second millennium B.C.E., in part on the basis of other anachronisms. Genesis 24, for example, calls Mesopotamia "Aram-Naharaim", which could not have been slipped in by a later copyist, for it is integral to the story. Laban is even called an Aramean in the Jacob stories (Genesis 28:5; 31:20, 24). But, according to Lemche, this is anachronistic because the region became Aramean "at the end of the second millennium B.C.E.", for the "earliest Assyrian sources do not mention the Arameans before the twelfth century B.C.E., and we possess no sources to support the existence of Arameans during the Late Bronze Age" (pages 62-63).
Lemche also thinks that Pithom in Exodus 1:11 is anachronistic. He says that Pithom, which means "house of (the god) Atum", first "appears as a city name around the Saite period (not before the seventh century B.C.E.)" (page 55). Lemche speculates that Pharaoh Neco of the seventh century captured and employed Jews who had been captured in battle (the battle in which the Egyptians killed Josiah), using them for their building projects.
On pages 119-121 of Israel in Egypt, conservative scholar James Hoffmeier talks about areas from the time of Rameses (the Late Bronze Age, which was long before the seventh century) that have been proposed as possible sites for Pithom because they focus on Atum. Hoffmeier also disagrees with the argument that Pithom in Exodus 1:11 is an anachronism on account of it being a city-name because "'store cities' are in reality storage facilities attached to temples or palaces and not sprawling urban-sized magazines." Lemche seems to base his "anachronism" argument on Pithom in Exodus 1:11 being a city-name, which implies that "Pithom" could have been used as a name for a temple (but not a city) before the seventh century B.C.E. For Hoffmeier, however, "Pithom" in Exodus 1:11 is not anachronistic precisely because it's talking about a supplement to a temple, not a full-fledged city.
I want to note one more thing, which isn't an anachronism: On pages 64-65, Lemche says that the stories in the Hebrew Bible are inaccurate when they present commoners appearing before royalty, for "Sovereigns avoided such audiences because strict social convention alone determined whether someone could come before the king or his court." I'd actually like to see evidence for this, though. Whether the Hebrew Bible is totally historically-accurate or is fiction, I'm doubtful that it would present commoners appearing before royalty if that were completely impossible. Plus, why can't the Bible serve as evidence for the customs and mores of ancient times?
UPDATE: On page 171, Lemche refers to an event that is discussed in the Late Bronze Amarna letters: "Initially, Pharaoh demands Aziru's appearance before him to verify his loyalty." But Aziru was the king of Amurru, and so, technically, he may not have been a commoner. But, on page 212, Lemche states that, in the "ideological topos" of the Hebrew Bible, Mesopotamia, and Ugaritic literature, "the king always sits at the gate where poor people, widows, and orphans can come to plead their cases." Lemche goes on to state that "the king acted as society's supreme arbiter" as the representative of the gods, which seems to imply a degree of historicity to the king sitting at the gate and hearing the pleas of commoners.2. On pages 41-42, Lemche says that the Joseph story was incorporated into the "narrative thread of the Pentateuch". This was done by mentioning Joseph's eleven brothers. In the story, all you need are "the good and the evil brothers and the innocent-victim brother"---meaning that you don't need all eleven. But, for Lemche, the story was made into an explanation for how the Israelites got into Egypt, and that's why it came to include all twelve brothers. Originally, it was your typical tale about "a hero in a fairy tale who rises to eminence in a foreign country"---such as the story of Daniel, or perhaps the Egyptian story about Sinuhe. But it was transformed into a part of a larger narrative, and it was also made pan-Israelite.