Here the original manuscript reads sin (that is, in the singular). When copying from 𝓞 into 𝓟, Oliver Cowdery initially wrote sin, then consciously inserted the plural s (the ink flow is heavier). The problem here is whether the singular sin in 𝓞 is one of scribe 3’s typical errors—namely, of accidentally dropping the plural s. In this instance, the plural use is clearly expected, but the singular sin will work.
When we compare this text to its biblical parallel, we find the following wording in the King James Bible:
Based on this parallel, the singular sin in the original manuscript of the Book of Mormon should be considered correct.
In fact, this same accidental change from singular to plural occurred in one other place in the text:
In this second case, the 1908 RLDS text restored the singular sin, the reading of the printer’s manuscript. Here in 2 Nephi 31:4 (unlike the case in 1 Nephi 10:10), Oliver Cowdery did not emend the singular to the plural.
Elsewhere the Book of Mormon text has only the plural sins (not sin) in the phrase “the sin(s) of the world”. Yet in all 15 of these other instances, there is no reference to the role of John the Baptist as there is in 1 Nephi 10:10 and 2 Nephi 31:4:
In three cases (Alma 5:48, Alma 7:14, and Alma 39:15), the text uses language nearly identical to John the Baptist’s (as in John 1:29), yet without mentioning him in any way. Thus the earliest text for 1 Nephi 10:10 and 2 Nephi 31:4 is perfectly consistent; only when a passage refers directly to John the Baptist baptizing the Lamb of God does the Book of Mormon text uses the singular sin, precisely like the language in John 1:29.
Summary: Both 1 Nephi 10:10 and 2 Nephi 31:4 specifically refer to John’s baptism of Jesus and have the singular usage “the sin of the world”, as found in John 1:29; all other instances of this phrase in the Book of Mormon take the plural (“the sins of the world”).