The original text of the Book of Mormon uses the -(e)th verbal ending for both singular and plural third person (rather than for only the singular, the standard biblical style). Here in Jacob 2:23, the 1830 typesetter dropped the -(e)th ending. In his editing of 𝓟 for the 1837 edition, Joseph Smith replaced the final th of begineth with an s, but the 1837 edition itself continued with the begin of the 1830 edition.
Generally speaking, the 1830 typesetter did not remove nonstandard uses of the -(e)th ending. Thus the 1830 reading for Jacob 2:23 might have been unintentional, especially since the typesetter left unchanged two other occurrences of this people followed by a verb ending in -(e)th:
Note further that no edition has ever removed the -(e)th ending from these two cases involving this people. In addition, there are places in the text where the verb for this people takes no inflectional ending:
In two of these cases (Mosiah 11:23 and Helaman 11:14) the lack of an inflectional ending for the verbs could be the result of the verbs being in the subjunctive rather than the indicative. But the other two cases are clearly indicative and omit the -(e)th ending. Also note that only the example here in Jacob 2:23 involves variation. We should probably treat the three original cases with the -(e)th ending as an instance of the biblical style rather than as a third person singular ending. In fact, Joseph Smith’s emendation to begins is nonstandard (“this people begins to wax in iniquity”).
The original text thus appears to be variable with respect to the phrase this people and the inflectional ending for the associated verb. This variability continues in the current text. Grammatical purists may want to remove the -(e)th ending in the two remaining cases involving this people, although one of these (2 Nephi 18:6) is a quote from Isaiah (which has the -(e)th ending in the King James Bible). Interestingly, 2 Nephi 27:25 also quotes Isaiah (namely, Isaiah 29:13), and there the King James Bible has draw, not draweth. So even the King James Bible shows variability in subject-verb agreement for this people. For further discussion of this issue, see under infl al endings in volume 3.
Summary: Restore the -(e)th ending for the verb begin in Jacob 2:23 (“this people beginneth to wax in iniquity”).