Notes on the Bible, by Albert Barnes, [1834], at sacred-texts.com
Deuteronomy Chapter 13
The admonition of the closing verse of the last chapter introduces a new series of warnings intended to serve as a further safeguard against violation of these duties. The true modes and forms of worship have been laid down: the next step is to legislate against the authors and abettors of false ones.
A prophet, or a dreamer of dreams - Compare Num 12:6. The "prophet" received his revelations by vision or direct oral communication Num 24:16; Sa2 7:4; Co2 12:2; "the dreamer of dreams" through the medium of a dream Kg1 3:5; Mat 2:13.
The Lord had said, "Thou shalt have none other gods but Me." A prophet is here supposed who invites the people "to go after other gods." To such a one no credit is under any circumstances to be given, even should he show signs and wonders to authenticate his doctrine. The standing rule of faith and practice had been laid down once for all - that the people were to hold fast. The prophet who propounded another rule could only be an impostor.
A different case is considered in Deu 18:18, etc.
The context and parallel passages (compare Deu 17:7; Lev 20:2) indicate that there was to be a regular judicial procedure, and that the manner of the execution was to be by stoning. In this the community was to take its part in order to show its horror at the crime, and to clear itself of complicity therein.
If thy brother, the son of thy mother, or thy son, or thy daughter, or the wife of thy bosom, or thy friend, which is as thine own soul, entice thee secretly, saying, Let us go and serve other gods, which thou hast not known, thou, nor thy fathers;
City was to keep jealous watch over city, as man over man. The clause "which the Lord thy God hath given thee to dwell in" significantly reminds them that the real ownership of their dwellings rested in the Lord (compare Lev 25:23), and that they, the mere tenants, must not allow His property to become a center of rebellion against His just authority.
In Deu 15:9 and in Nah 1:11 the word "Belial" is rendered in our translation by the adjective "wicked." The word means "worthlessness."
(from Barnes' Notes)
Every whit, for the Lord thy God - Some prefer: "as a whole offering to the Lord thy God."