Here we have some confusion in the original manuscript over the number for border and shore. Both were initially written in the plural (“by the borders near the shores of the Red Sea”), then Oliver Cowdery corrected both to the singular (“by the border near the shore of the Red Sea”), although in the case of border(s), Oliver may have attempted to restore the plural s after having crossed it out. The plural s in shores is crossed out with only somewhat heavier ink flow and probably represents a correction made when Oliver read the text back to Joseph Smith. But the plural s in borders seems to be crossed out with excessively heavier ink flow. In fact, the crossout is shaped such that it could be interpreted as Oliver’s attempt to put the s back in, with the result that the crossout looks much larger than a regular crossout. In other words, the final intended text could well have been “by the borders near the shore of the Red Sea”.
Later, when he copied from 𝓞 into 𝓟, Oliver Cowdery wrote borders rather than border. Perhaps he was able to figure out that his ultimate correction of border(s) was supposed to be the plural borders. Or perhaps he simply expected the plural borders. In any event, the printer’s manuscript reads “by the borders near the shore of the Red Sea”. And this use of plural borders and singular shore has continued throughout the printed editions.
Elsewhere the text consistently uses the plural borders (75 times), although in a couple of cases in the printer’s manuscript, the scribe initially wrote the singular border:
Thus we see a scribal tendency to accidentally write the singular border instead of the correct borders. In any case, the plural borders seems to be the consistent usage in the Book of Mormon. Determining the expected number for shore is more complex. There are three occurrences of shore(s), excluding cases of seashore: namely, the one here in 1 Nephi 2:5 plus two others right next to each other in the book of Ether:
The first occurrence is in the singular, the second in the plural, yet in both instances we have exactly the same phraseology: “upon the shore(s) of the promised land”. The scribal correction in 1 Nephi 2:5 of shores to shore implies a tendency on Oliver Cowdery’s part to write shores instead of shore. One possibility then is that in Ether 6:12 Oliver once more accidentally wrote shores instead of shore, but this time he didn’t catch his error.
One could further argue for the singular shore by considering the word seashore. This related compound occurs in the text only in the singular (26 times) and without any scribal tendency to miswrite it in the plural. However, evidence from the related seashore may be irrelevant to determining the number for shore(s). As David Calabro points out (personal communication), the plural seashores seems unacceptable on its own, while both shore and shores are possible. In addition, there are only three examples of shore(s), so the internal evidence is weak for emending shores to shore in Ether 6:12. Thus it is probably best to leave the variation between shore and shores in the Ether passage.
Summary: The intended reading in 1 Nephi 2:5 appears to be “by the borders near the shore of the Red Sea”; this is the reading in 𝓟, and Oliver Cowdery’s corrections in 𝓞 can also be read this way; Ether 6:12 may have originally read so that the singular shore occurred both times in the phrase “upon the shore of the promised land”, but the evidence for such an emendation is meager.