Doug, hope this will help. There was a Bethel lecture on the subject. Some here might still have it on their files. The following is based on Dan. 9:24. If I remember correctly, this first part comes from the Keil-Delitzsch Commentary of above verse. The source of the rest of the quotes are noted.
To make atonement for error. The third statement is, כִּפֶּר is terminus techn., to pardon, to blot out by means of a sin-offering, i.e., to forgive.
These three passages thus treat of the setting aside of sin and its blotting out; but they neither form a climax nor a mere συναθροισμός, a multiplying of synonymous expressions for the pardoning of sins. Against the idea of a climax it is justly objected, that in that case the strongest designation of sin, הַפֶּשַׁע, which designates sin as a falling away from God, a rebelling against Him, should stand last, whereas it occurs in the first sentence. Against the idea of a συναθροισμός it is objected, that the words “to shut up” and “to seal” are not synonymous with “to make reconciliation for,” i.e., “to forgive.” The three expressions, it is true, all treat alike of the setting aside of sin, but in different ways. The first presents the general thought, that the falling away shall be shut up, the progress and the spreading of the sin shall be prevented. The other two expressions define more closely how the source whence arises the apostasy shall be shut up, the going forth and the continued operation of the sin prevented. This happens in one way with unbelievers and in a different way with believers. The sins of unbelievers are sealed, are guarded securely under a seal, so that they may no more spread about and increase, nor any longer be active and operative; but the sins of believers are forgiven through a reconciliation. The former idea is stated in the second member, and the latter in the third, as Hofmann and Kliefoth have rightly remarked.
There follows the second group of three statements, which treat of the positive unfolding of salvation accompanying the taking away and the setting aside of sin.
*
Making atonement. וּלְכַפֵּ֣ר from כפר, to cover, to atone.
Etymology: The lexica of the nineteenth century associated Heb. kipper with Arab. kafara, “cover,” describing the act of atonement as the covering of guilt. Since Heinrich Zimmern’s reference to Bab. kuppuru, the two etymologies agree.
In the Koran, Arab. kaffara, “absolve” (with God as subject), is a term borrowed from Judaism but given a new semantic structure: atonement is an act of the merciful God, without the need of any sacrifice. Arabic lexicographers derive the word from kaffara, “cover,” so that kaffara may have overtones of “atone (by covering).”
The use of kesāyā, “cover,” to translate kappōreṯ in 4Q156 presupposes a specific concept of the sacral object called kappōreṯ; it is not an etymological conjecture. The interpretation of kipper as “cover” on the basis of Arabic, most recently supported by Stamm, is fraught with problems.
In the LXX, words based on the root kpr are translated consistently by derivatives of hiláskomai; “propitiate, appease.” The regular equivalent of kipper is exiláskomai; the Day of Atonement is translated hēméra exilasmoú (Lev. 23:27f.); the sacral object termed kappōreṯ is translated hilastḗrion; kōṗer is translated exílasma (1 Sam. 12:3; Ps. 49:7 [LXX48:8]).
a. The construction of exiláskomai carefully imitates that of kipper.
b. The usage is described as a semitism; it does not agree with common Greek idiom.
c. Contrary to a popularly accepted theory, certain other translations of kipper – in particular apaleíphō (Dnl. 9:24, possibly a double translation in conjunction with exiláskomai), “wipe away” – cannot be cited in support of the basic meaning of “cover” for kipper.
d. The variety of translations for kōṗer is noteworthy, especially lýtron (Prov. 6:35; 13:8; pl. in Ex. 21:30; 30:12; Num. 35:31f.), “ransom” or “to free by ransom” (cf. Ex. 13:13).
e. In the CGS we notice a rare word ảntílutron, “corresponding ransom,” at 1 Tim. 2:6, a statement based on Matt. 20:28 and Mark 10:45 (cf. Tit. 2:14). See TDOT, vol. VII, pp. 289-292; TDNT, vol. IV, p. 349.
For error. To err, to deviate, to incur guilt. עָוֹ֔ן from עָוָה. Influenced by the efforts of earlier lexicographers to derive every Hebrew word from a basic material meaning, GesTregLex viewed `wh as a union of two Arab. verbs `wy “bend, turn” and ģwy “deviate, err from the path,” which in turn corresponds to Eth. `awawa, “err, stray, not know.”
R. Knierim thus deduces a basic meaning of “bend, curve, turn aside, twist.” Even if this etymological meaning is correct, one still cannot determine whether any biblical writer was familiar with the original meaning. In any event, the use of the individual conjugation stems already shows that the root expresses a “dynamistic holistic thought” that tries to conceive in a single sweep “the various phases of a misdeed-consequence process (deed-consequence completion).”
In older traditions, `āwōn occurs approximately 20 times as a “vernacular term… qualified by a dynamistic understanding of reality.” In the majority of instances it refers to the transgressions of human beings toward others, errors inevitably prompting drastic consequences for the perpetrator. It is closely related to “sin” (cf. 1 Sam. 20:1; 2 Sam. 24:10), its opposite being ḥeseḏ (cf. 2 Sam. 3:8). The reference is thus to fateful guilt caused by a person’s iniquitous transgressions; neither “guilt” nor “sin” nor “punishment” provides an adequate translation in such cases.
God is the only entity capable of turning away such burden of guilt from a perpetrator, thereby bringing about a positive outcome. He either takes away `āwōn from a sinner (cf. 2 Sam. 24:10) or can permit atonement. The people confess chāṭā’nû; in later texts `āvînû is added for the sake of completeness (Dnl. 9:5; cf. 2 Chron. 6:37). See TDOT, vol. X, pp. 547-549, 550-552.
It think this was how the Witnesses saw it. Things might have changed. I am not up-to-date with current Witness theology.
To finish off sin as well as making atonement for error. Jesus’ being cut off in death, his resurrection, and his appearance in heaven resulted in ‘finishing off sin as well as in making atonement for error’ (Dan. 9:24). The Law covenant had exposed the Jews as sinners, condemned them as such, and brought upon them the curse as covenant breakers. But where sin “abounded” as exposed or made evident by the Mosaic Law, God’s mercy and favor abounded much more through his Messiah (Rom. 5:20). By Messiah’s sacrifice, transgression and sin of the repentant sinners can be cancelled and the penalty thereof be lifted. Interestingly, the life course of the Isaiah’s Suffering Servant would result in him “being pierced for our transgression; he was being crushed for our errors… because of his wounds there has been a healing for us… despite the fact that he had done no violence and there was no deception in his mouth” (Is. 53:5, 8).