"This covenant [of grace] is revealed in the gospel; first of all to Adam in the promise of salvation by the seed of the woman, and afterwards by farther steps, until the full discovery thereof was completed in the New Testament" (Second London Baptist Confession of Faith, 1689, chapter 7:3)
Samuel Renihan (@Petty_France) recently tweeted a ten point summary of Thomas Goodwin's view of the Mosaic Covenant. I've reproduced the list below. Goodwin's stance bears more than a passing resemblance to that of his fellow Independent and good friend, John Owen. Owen's understanding of the Mosaic Covenant was highly influential in Particular Baptist circles. Renihan has dealt with this at length in his excellent, From Shadow to Substance: The Federal Theology of the English Particular Baptists (1642-1704), Regent's Park College, 2018. In essence Goodwin, Owen and many Particular Baptists held that the Mosaic Covenant was a covenant of works that was subservient to the covenant of grace. This line of thought is certainly compatible with the Second London Baptist Confession, but it is not explicitly taught in that document.
In his more recent The Mystery of Christ: His Covenant And His Kingdom, Founders Press, 2019 or Broken Warfe (UK edition), Renihan make this distinction between a covenant of works and a covenant of grace, "In a covenant of works, when obedience has been rendered, blessings promised are enjoyed. Conversely, in a covenant of grace, after promises have been received, laws are introduced." But on that basis, was the Mosaic Covenant really a covenant of works? Did the Lord redeem Israel from Egypt and promise them the land of Canaan on the basis of obedience rendered? I think not.
The Mosaic Covenant was a further elaboration of the Abrahamic Covenant especially formulated for Israel's life in the Promised Land, Exodus 3:1-8. The law was given to Israel as God's redeemed people, Exodus 20:1-2. It was as such that Israel entered into a solemn covenant with the Lord and promised to obey him, Exodus 24:3. The covenant was ratified by the shedding of blood without which there is no forgiveness of sins, Exodus 24:6-8, Hebrews 9:18-22.
Should Israel renege on their covenant obligations they were threatened with exile from the Promised Land (Deuteronomy 28). But that does not make the Sinai Covenant a covenant of works. Unlike with Adam, there was a way back for Israel from the dark paths of sin, Leviticus 26:40-45.
But neither does this mean that the old covenant was an administration of the covenant of grace, as taught in the Westminster Confession of Faith (Chapter VII:V). It was not. For one, the covenant of grace is with Christ and his elect people. The old covenant was with Abraham and his descendants, but 'not all who are descended from Israel belong to Israel' (Romans 9:6). Among the people of Israel only a remnant were chosen by grace for salvation through the coming Messiah, Romans 11:5). The Abrahamic, Mosaic and Davidic covenants were 'covenants of promise' (Ephesians 2:12) wherein the covenant of grace was revealed, "until the full discovery thereof was completed in the New Testament".
With those thoughts in mind I will offer a brief comment on each of Goodwin's points on the Mosaic Covenant as summarised by Renihan.
1. It was a promulgation of the covenant of works - no. The Mosaic covenant was not a republication of the covenant of works with with Adam. Life in the Promised Land was not granted to Israel on the basis of their righteous obedience, Deuteronomy 7:6-8, 9:5. Neither was it an administration of the covenant of grace. It was a 'farther step' in the revelation of salvation promised in Christ.
2. It was based on a redemption other than Christ's - yes, the exodus, which typified Christ's redemption, Colossians 1:12-14.
3. It had a Mediator other than Christ - yes, Moses, who foreshadowed the work of Christ as mediator of the new covenant, Hebrews 3:1-6.
4. It offered a sanctification other than Christ's - 'I am the Lord who sanctifies you' (Leviticus 20:8). Israel was set apart as God's holy nation by virtue of the Lord's electing love and redeeming power. Israel's holiness was to manifest itself as the nation was devoted to God in obedience to his commands. These commands included ceremonial rules such as the food laws of Leviticus 11 and regulations concerning bodily discharges in Leviticus 15. But Israel was also called to pursue an inward holiness that was only possible by the work of the Spirit, Psalm 24:3-6, Ezekiel 36:25-28. Israel's role as a 'holy nation' to the Lord was a shadowy picture of the sanctifying work of Christ by the Spirit under the new covenant, 1 Peter 1:1-2, 14-19, 2:9-10.
5. It gave a justification other than Christ's. What does this even mean? Under the Abrahamic and Mosaic covenants justification was by faith in the promised Christ, Gen 15:6 (Romans 4:1-5), Psalm 32 (Romans 4:6-7). The Law and the Prophets of the old covenant bore witness to the righteousness of God apart from the law by faith in Christ, Romans 3:21-22.
6. It promised an earthly life and inheritance. Yes, which was typical of the eternal inheritance of the saints, 1 Peter 1:3-5.
7. Unregenerate Jews could keep the covenant. No, to do that their hearts needed to be circumcised, Deuteronomy 10:12-16, 30:6. That was only the case for a godly remnant, which was why Israel as a whole broke the covenant and was exiled from the land. The unregenerate could not live up to the law's demands and stood condemned for their disobedience (Romans 8:3a, Galatians 3:10-11). By way of contrast the new covenant was 'not of the letter, but of the Spirit. For the letter kills, but the Spirit gives life.' (2 Corinthians 3:6).
8. It was typical of the covenant of grace. How is this compatible with point 1? The Mosaic covenant is typical of the covenant of grace only because it was graciously made with Israel as a covenant of promise. The types and shadows of the old covenant point to Christ, the antitype and substance, Hebrews 8:5-6, Colossians 2:16-17.
9. It was subservient to the covenant of grace. Yes. Its function was to prepare the way for Christ and then get out of the way once the mediator of a new and better covenant had come, Galatians 3:23-25, Hebrews 8:13.
10. It was "truly, and toto genre, differing from" the covenant of grace. Yes, because a promise is different from its fulfilment, a type is different from an antitype and a shadow different from the substance. The temporary old covenant was indeed different from the eternal covenant of grace which was finally and fully disclosed in the new covenant.