The following is from the KJV of Romans 16:16:
Salute one another with an holy kiss. The churches of Christ salute you.
If you check the JST footnote to the word "kiss," Joseph Smith rendered it as "salutation." (Also, it is worth noting that both the NRSV and NIV render this word as "kiss.")
So what is JS getting at here? According to the typical understanding I described above, it seems that he was restoring the original, less sexualized form of greeting among fellow believers (perhaps in reference to the temple?) instead of some kind of kissing ritual that was added by some licentious scribe.
Except for this and this.
So what should we make of this discrepancy? My own hypothesis is that many of the JST corrections/additions/etc., where meant to do exactly what most of us seem to think they do, restoring some original sense of the text or understanding that was lost. In other instances, such as the example from Romans cited above, I think that JS had a particular agenda he was pursuing (and I mean agenda in the least manipulative, smoke-filled-room sense possible), namely a didactic or exegetical agenda as to how the Latter-day Saints ought to live. Therefore, changing "kiss" to "salutation" may not be an assertion by JS that early Christians did not, in fact, kiss to greet one another, but rather that Latter-day Saints should prefer a salutation as a method of greeting one another.
I don't want to go into too many more examples of this, but I found another one yesterday while studying the scriptures with my wife. Look at footnote a to Hebrews 5:7. JS indicates that this is a verse about Melchizedek and not Christ. Admittedly, the textual evidence (in both Greek, Latin, and English) does not suggest this interpretation, and from my own personal experience, neither does a reading of the verse itself in context. In my own opinion, I think most people, LDS and non-LDS alike, see an allusion to Christ here. Furthermore, BRM pointed out in his Doctrinal New Testament Commentary that this was actually about Melchizedek AND Christ. So why does JS insist that it is not Christ, but Melchizedek? Again, I think it is an exegetical agenda. JS wanted to give the Latter-day Saints more information about Melchizedek the prophet, to add background to the narratives he was revealing regarding Abraham, Moses, and the Priesthood. As BRM points out, since Melchizedek is a type of Christ, there is nothing to suggest that this scripture necessarily must be about Christ, or Melchizedek, but not both of them.