Ross Geddes (personal communication, 24 July 2006) suggests that the the preceding the first instance of “wickedness and abominations” is an error for their. Note that later in this verse we have an instance of “their wickedness and abominations” but without a preceding all (the second instance of “wickedness and abominations”). Of course, all their is possible in this context, as in Alma 37:21: “all their wickedness and abominations”.
With respect to the use of the in Mormon 2:18, both 𝓟 and the 1830 edition read alike, so 𝓞 must have also read the. Nonetheless, there is considerable evidence elsewhere in the manuscripts for mixing up the and their; see, for instance, under Alma 27:23 for evidence that Oliver Cowdery frequently replaced their with the (Oliver is the presumed scribe here in 𝓞).
The use of the definite article the normally implies some kind of postmodification, as in 3 Nephi 9:9: “because of their sins and their wickedness which was above all the wickedness of the whole earth”. One could assume in Mormon 2:18 some kind of ellipsis after “all the wickedness and abominations” (perhaps one with the meaning ‘which I have been describing’). Later in this verse one can find some support for a more general interpretation of “wickedness and abominations”, in the third instance of “wickedness and abominations” (where there is no determiner at all before this phrase):
Another possible emendation in Mormon 2:18 would be to replace the the with this: “I did make a full account of all this wickedness and abominations”. Support for the use of this in this context can also be found elsewhere in the text: “yea for all this wickedness they were punished” (Alma 30:10). Nonetheless, one wonders if a this in Mormon 2:18 wouldn’t also require abominations to be in the singular, as in Jacob 2:16: “this iniquity and abomination”.
In any event, the use of the for the first instance of “wickedness and abominations” in Mormon 2:18 is not impossible, although it may very well be an error. Since the interpretation involving ellipsis will work, the critical text will maintain the earliest reading with the. Nonetheless, there is a chance that the the is an error for their (or perhaps even this).
Summary: Maintain in Mormon 2:18 the use of the in the phrase “all the wickedness and abominations”, the reading of the earliest textual sources; the definite article may be an error for their (or maybe this), but since this phrase can be interpreted as involving ellipsis, the critical text will leave it as it is.