Why does it say that the man was old?
Malbim: After teaching the evil of the residents (none of the residents offered to take him in), it teaches the merits of this man. He took him in, even though (a) he was old, (b) he came just now, (c) he was working [hard] in the field, and (d) he was only Gar (staying temporarily) in Giv'ah; he was not a fixed resident.
Why does it say "Bnei Yemini"?
Radak #1: This teaches that Giv'ah was of Binyamin, for there was another Giv'ah (hill) with a city in it. Above (14) it says "ha'Giv'ah Asher l'Binyamin."
Radak #2: Some say that this means that they were established to be evil 1 ; their deeds prove so.
What is the source that "Yemini" refers to evil? In one Perush, Yefe To'ar (on Bereishis Rabah 37:2) says that "Kush ben Yemini" (Tehilim 7:1) refers to Edom, which was Yamin (south) of Eretz Yisrael. (It clearly refers to one who afflicted David or Yisrael. The primary opinion holds that it refers to Sha'ul. - PF)