What is the LDS church's stance on the curse of Cain? Since the restoration, the LDS Church has taught that certain dark skinned people were cursed to be cut off from the presence of the Lord:


  20 Wherefore, the word of the Lord was fulfilled which he spake unto
  me, saying that: Inasmuch as they will not hearken unto thy words they
  shall be cut off from the presence of the Lord. And behold, they
  were cut off from his presence.


And that their darks skins were a sign of the curse so that they could be recognized as being cursed:


  21 And he had caused the cursing to come upon them, yea, even a sore
  cursing, because of their iniquity. For behold, they had hardened
  their hearts against him, that they had become like unto a flint;
  wherefore, as they were white, and exceedingly fair and delightsome,
  that they might not be enticing unto my people the Lord God did cause
  a skin of blackness to come upon them.
  
  22 And thus saith the Lord God: I will cause that they shall be
  loathsome unto thy people, save they shall repent of their iniquities.
  
  23 And cursed shall be the seed of him that mixeth with their seed;
  for they shall be cursed even with the same cursing. And the Lord
  spake it, and it was done.  (2 Nephi 5:21-23)


Today, the official stance of the church is this:


  "Today, the Church disavows the theories advanced in the past that
  black skin is a sign of divine disfavor or curse, or that it reflects
  unrighteous actions in a premortal life; that mixed-race marriages are
  a sin; or that blacks or people of any other race or ethnicity are
  inferior in any way to anyone else. Church leaders today unequivocally
  condemn all racism, past and present, in any form." (Race and the Priesthood)


Does this mean that the Church is disavowing that people of African descent were ever cursed and bore the sign of the curse? Or does this mean that since the curse was lifted, and in 1978 when the Preisthood was officially offered to all worthy males, that the "sign of the curse" was no longer a sign of anything except mortal heritage, and that those spirits being born with those phenotypes today are no longer born to those lines based on premortal favour?
People might assume that all black people are cursed.  Although there are some recorded instances that having black or dark skin is the result of a curse from God, it should under no circumstances always be assumed as such.  This is simply an error of extrapolation.

The statement you quote from LDS.org was, is, and will always be correct.  Black skin is not a sign of divine disfavor or curse.  It is sometimes associated with people who have been cursed in the scriptures, but it does not necessarily signify a curse, hence the claim.

This is what the KJV (the Bible text accepted by the Church of Jesus Christ) says about the mark put on Cain:


  15 And the Lord said unto him, Therefore whosoever slayeth Cain,
  vengeance shall be taken on him sevenfold. And the Lord set a mark
  upon Cain, lest any finding him should kill him.
  
  Genesis 4:15


It appears the mark was not part of the curse, but rather served as a warning to others so they would not kill him.  Later this mark was indeed used to identify the descendants of Cain so Adam's other descendants wouldn't mix with them.  The descendants of Cain were actually black, and it is implied through the footnotes that this is the same as the mark.  However, this apparent racism was reconciled through Christ:


  33 For none of these iniquities come of the Lord; for he doeth that
  which is good among the children of men; and he doeth nothing save it
  be plain unto the children of men; and he inviteth them all to come
  unto him and partake of his goodness; and he denieth none that come
  unto him, black and white, bond and free, male and female; and he
  remembereth the heathen; and all are alike unto God, both Jew and
  Gentile.
  
  2 Nephi 26:33


In any case, it would be good to confirm that blacks are in fact descendants of Cain before making assumptions about curses and marks involving Cain.

Members of the LDS faith reconcile apparent discrepancies (particularly in Church teachings) by trusting in God regardless of their doubts and by remembering that the leaders of the Church are imperfect humans.  While the president of the Church is promised never to lead it astray, many many leaders (in ancient times as well as present) have (sometimes even innocently) said and done things that were very incorrect.  Not everything all Church leaders say is doctrine.  This is simply part of the life experience.  As much as we would all like our Church organization to be perfect, it simply isn't, and there's little use in pretending it is.