When copying from 𝓞 into 𝓟, Oliver Cowdery accidentally skipped the conjoined predicate “and rehearsed unto them”, probably because his eye skipped from the preceding unto them to the following one as he copied the text (“many things unto them and rehearsed unto them”). The 1981 LDS edition restored the phrase. Without that phrase, the following noun phrase “how great things the Lord had done for them” seems stranded and must therefore be interpreted as an appositive to the previous “many things”. Whenever it occurs in the text, “how great things” always complements a main verb:
Thus a verb is definitely expected in 2 Nephi 1:1.
Joseph Smith himself did not restore the phrase “and rehearsed unto them” in his editing for the 1840 edition. As noted earlier, there are four places in that edition where Joseph restored phrases from 𝓞 that Oliver Cowdery had accidentally omitted in his copying from 𝓞 into 𝓟: “the name of ” in the 1 Nephi preface, “and partake of the fruit” in 1 Nephi 8:18, “for all men” in 1 Nephi 10:18, and “with sorrow” in 1 Nephi 18:18. All four of these are in 1 Nephi; thus it appears that Joseph’s checking of the text against 𝓞 did not continue much past the first book.
Summary: Maintain the reading of the original manuscript in 2 Nephi 1:1 (“and rehearsed unto them how great things the Lord had done for them”).