Edwards references the problem of continuity between the Testaments in An Humble Inquiry (Works 12:280). This was a problem for him as those in favor of the Half-Way Covenant and Stoddardeanism appealed to the Mosaic Law for church precedent, e.g. the Law’s allowing all members of the nation to come to the passover sacrifices.
There is perhaps no part of divinity attended with so much intricacy, and wherein orthodox divines do so much differ, as the stating of the precise agreement and difference between the two dispensations of Moses and of Christ. And probably the reason why God has left it so intricate, is, because our understanding the ancient dispensation, and God’s design in it, is not of so great importance, nor does it so nearly concern us. Since God uses great plainness of speech in the New Testament, which is as it were the charter and municipal law of the Christian church, what need we run back to the ceremonial and typical institutions of an antiquated dispensation, wherein God’s declared design was, to deliver divine things in comparative obscurity, hid under a veil, and involved in clouds?
For more on this, one can see Edwards’ Miscellany 1118 on “Dispensations” (account required).