en.wikipedia.org/wiki/Herod_the_Great

This sentence misstates Josephus.

In Antiquities 14, Josephus introduces Herod’s father Antipater as "an Idumean" and says Nicholas of Damascus claimed descent from Jews who came from Babylon "but that assertion ... was to gratify Herod"—i.e., Josephus does not endorse that alternative genealogy. Josephus then continues by tracing Antipater through his father Antipas, an Idumaean notable.

A standard reference work summarizing Josephus makes the same point explicitly: "Josephus states that Antipater I belonged to a distinguished Edomite family" and says Nicholas of Damascus’s Jewish-descent claim "is denied by Josephus."

So the article’s wording is incorrect in two ways:

1. It attributes to Josephus a genealogy from Eleazar Maccabeus / the Hasmoneans that Josephus does not give.
2. It says this made Herod "half-Jewish," whereas Josephus’ own presentation is that Herod’s paternal family was Idumaean/Edomite and that claims of Jewish ancestry were later apologetic claims, not Josephus’ accepted genealogy.

The year in this sentence is off by one.

Reference works and chronologies place Herod’s trip to Rhodes after Actium, in 30 BCE. The Encyclopedia of the Bible dates it to "spring, 30 b.c." Likewise, Attalus’ year-by-year ancient chronology lists "Herodes meets Octavianus in Rhodes" under 30 B.C.

So while the meeting at Rhodes did happen, dating it to 31 BCE is incorrect; the encounter is placed in 30 BCE.

This compresses Salome’s inheritance into the wrong geography.

Josephus says that Salome received Jamnia, Ashdod/Azotus, and Phasaelis. That already shows the territory was not just a single small holding "in the Gaza region." More importantly, Phasaelis was a Herodian estate in the Jordan Valley north of Jericho, far from Gaza.

So the statement is geographically inaccurate: Salome’s holdings were a set of towns/estates including one in the Jordan Valley, not merely a toparchy "in the Gaza region."