In the English language, nouns traditionally have no gender. I guess words like actor/actress, waiter/waitress clearly indicate a gender, but the point is that in many other languages, the article preceding any noun indicates what gender it is. This is not the case in English. In my native language, for example, there are 3 genders: Masculine, feminine and neuter. In Hebrew, there are two, masculine and feminine. Every noun will have a gender. When translated into English, this characteristic is typically lost. But there are some cases in the Book of Mormon, where a gender pronouns refers back to the noun, especially when it is feminine, it seems. (This may also be due to the fact that the feminine nouns are easier to find with searches. I found some searching for "she/her" but couldn't do the same with "he/him/his" because there are way too many results).
So there may be more, but I have found at least the following:
Wisdom
In Mosiah 8:20, we read:
how and impenetrable are the understandings of the children of men; for they will not seek wisdom, neither do they desire that should rule over them!
Since nouns have no gender in English, there is no reason why wisdom should be referred to as something feminine. Unless you consider the original Book of Mormon language, based on Hebrew, where wisdom is a feminine noun. In fact, wisdom is associated with the devine feminine, and the way it is even personified in this verse is a strong allusion to that concept.
City
wo be unto this great city, because of the wickedness and abominations which are in her.
Similarly, in Mormon 4:14
And they did also march forward against the city Teancum, and did drive the inhabitants forth out of her
So apparently, cities are regarded as feminine nouns in the Book of Mormon too.
Vessel/ship
Having little to no knowledge of the Hebrew language, I'm relying on Strong's Hebrew at biblehub.com. This one was a bit tricky but the most common word for "ship" in the Hebrew Old Testament (31 occurrences) is oniyyah, which is a feminine noun. There was another masculine noun, tsiy, but it had only 4 occurrences. In the Book of Mormon, ship is feminine:
And it came to pass that one other ship also did sail forth; and whither she did go we know not. (Alma 63:8)
There is another case in Mormon 5:18, when the word, "vessel", is used, but clearly in the meaning of a ship.
as a vessel is tossed about upon the waves, without sail or anchor, or without anything wherewith to steer her; and even as she is, so are they.
The only Hebrew word I found that is translated into "vessel" but defined as "ship" is sephinah. This is also a feminine noun in Hebrew. However, there is only one occurrence of this word (Book of Jonah).
Earth
In Helaman 11:13, we read
O Lord, wilt thou hearken unto me, and cause that it may be done according to my words, and send forth upon the face of the earth, that she may bring forth her fruit, and her grain in the season of grain.
Again, there are several possible candidates for the word, "earth", in Hebrew. I think the best candidate by far is erets, another feminine noun. Other candidates are Aramaic or have very few occurrences but most of these are also feminine. "Aphar" is masculine and can be translated into "earth" but in the sense of "soil/ground", which does not fit the context in Helaman.
Justice
For behold, justice exerciseth all his demands (Alma 42:24)
So it is in Hebrew. There are several candidates, like din, tsedeq and meshar but they are all masculine.
Mercy
and also claimeth all which is her own (Alma 42:24)
I learned a lot by studying the possible Hebrew root of this passage. John W. Welch notes here that
The words mercy and justice in Hebrew have gender. Wisdom and mercy are represented by female concepts, whereas justice is often male.
The underlying Hebrew origin (even though Alma surely didn't speak the same kind of Hebrew that we find in the Old Testament) is likely racham, even though no Hebrew word directly translates to mercy. Racham is better translated into compassion, in which case it actually is a masculine noun. But it also means womb and is then a feminine noun connected to women and often childbirth. The two meanings might seem very unrelated, but the Hebrew idea is that this compassion comes from deep within and is perhaps best illustrated by the feelings of a mother for her child. This actually adds some meaning to "bowels of mercy" that we find several places in the Book of Mormon. It seems likely that this expression originates from the Hebrew "racham". In Alma 34:15, we read
to bring about the bowels of mercy, which overpowereth justice
This is Alma 42 language and the reason why I believe "mercy" in this chapter is somehow related to the Hebrew "racham".
In Hosea 1:6, Hosea's daughter was to be named Lo-Ruchamah, meaning no mercy/compassion. Later in Hosea, the name is changed to "ruchama" as the Lord symbolically turns his anger to mercy. Ruchama is still today a Jewish female name. So even though it technically can be a masculine noun, it is very much a feminine concept in ancient Hebrew.
This is just one of numerous examples of small details in the Book of Mormon that provide evidence of its ancient origins. If Joseph Smith had made it up, we could perhaps explain away one or two of these as lucky guesses and get away with it, but there are 6 nouns in this list. To compare with my native language, earth is feminine, ship is neutral and city is masculine. The rest are words that usually would not be preceded by an article and therefore a bit undefined in terms of gender, but if you were to use an article, they would all be masculine. This is quite different from the noun genders we see in the Book of Mormon that match better with Hebrew than Greek, Latin or other more modern languages assigning gender to nouns.