Critics cite Deuteronomy (18:20-22) in an attempt to show that if a man makes a prophecy and it does not come to pass then he is a false prophet. So I just want to quickly say something about that. The verse in question is about the origin of the prophecy, not the origin of the prophet. Moreover, Jeremiah 18:7-10 gives us at least one reason why God may reverse a prophecy. And there's nothing to say that reason is the only valid reason God could have. So, God can change and reverse prophecies after they are given.
The most important thing is to accept the Lord's statements on His terms. For instance, when God told Abraham to sacrifice Isaac, and instructed him how to do so, God actually wanted Abraham's sacrifice to happen in his heart, not to actually result in a physical sacrifice of Isaac. This is the same principle behind the statement that when a man looks on a woman to lust after her, he has "already committed adultery" in his heart. Just because we don't see something be fulfilled physically doesn't mean it wasn't fulfilled in the Lord's eyes.
The first prophecy I would like to discuss is the prophecy on war in section 87 of the D&C. Ironically, many of us use this section as evidence of a fulfilled prophecy. But critics say that aspects of the prophecy were not fulfilled and that the part which was fulfilled is not impressive, that the civil war was somewhat expected decades before it started, and that the prophecy of it starting with the rebellion of South Carolina is not unexpected.
Joseph Smith’s prophecy was much bolder than critics give it credit for. Joseph Smith prophesied of not just a civil war but of something which was totally unprecedented in world history, i.e. a world war. No one else was predicting world war. The first line of the prophecy speaks of "wars," plural, which will "shortly come to pass." It says the wars will begin at South Carolina, but that doesn't mean each war had to begin there, only the first of the plural wars. The other wars would follow in a domino fashion.
Critics are off-base in dismissing the prophecy as being about a war everyone expected.
One part of the prophecy states that Great Britain "shall also call upon other nations, in order to defend themselves against other nations." This was literally fulfilled by Winston Churchill and may have even been fulfilled in WWI. The prophecy continues, explaining that "then" would war be "poured out upon all nations." This was fulfilled, as the war "then" went global.
Now, why would Joseph Smith in his day have reason to think that Britain, the largest empire in history, would be attacked by anyone and would need to call for help?
As far as the Civil War goes, the South did receive some aid from Britain in the form of war vessels. But note that the revelation does not say that any other nations would formally heed the call for help. It says the Southern States will call upon other nations, which they did - and those talks had the effect of promoting a widespread mood of instability, as they saw what was happening in the U.S. leading in time to the domino effect. In particular, France greatly feared the annexation of the Southern German States by the Northern German Confederation, and did not play its hand very well in attempting to prevent their unification. It would be natural for France to see a parallel between the North/South unification of the United States and the North/South unification of the German States. Likewise, Germany may have seen that parallel - although it achieved unification by fighting alongside rather than against its southern states. Once Germany was unified in 1871, constituting the Second Reich, the stage began to be set for WWI, which in turn led to WWII.
The prophecy also says that, after many days, "slaves shall rise up against their masters, who shall be marshaled and disciplined for war." This is often assumed to be a reference to black slaves. But the prophecy specifically says, "after many days." I think this is a reference to what happened after WWII as the Jews and others who had been slaves to the Nazis "rose up" against them, exposing the atrocities and leading to the discipline of many Nazis, just the prophecy states - that the masters "shall be marshaled and disciplined for war." Moreover, the original version crossed out “slaves” and read differently: “Those who are held in bondage shall rise up against those who hold them in bondage.”
Then the prophecy says that "remnants who are left of the land will marshal themselves, and shall become exceedingly angry, and shall vex the gentiles with a sore vexation."
Note the reference to both those who will be vexed (meaning greatly agitated) and those who will be the cause of the vexation. If it is gentiles who will be agitated, then it must be non-gentiles who will be the cause of the agitation. This breakdown between gentile and non-gentile obviously doesn't fit anything in the slavery situation of the United States.
But it fits perfectly with Israel, whose very existence vexes the gentile nations around it.
This fits perfectly with what we have seen happen with the Jews who were left after WWII, the formation of Israel and the great and final war before the Second Coming, wherein all nations will fight against Israel. To "vex" means to greatly agitate, and we have seen gentile nations become "vexed" by Israel - although I don't think Israel is the primary instigator, I think this part of the prophecy is still being fulfilled.
Second, let's look at D&C 84. In verses 2-5, the Lord commands the Saints to build a temple. But that temple was never built, so some people call this a false prophecy. However, six years after the commandment was given, it was revoked - see D&C 124:51. The Lord spiritually accepted the offering of the Saints, just as the Lord accepted Abraham's offering of Isaac, which He had commanded to be offered even though He knew it would not happen.
The Lord said the temple "shall be built," and it wasn't built, but the Lord also said "thou shalt not kill" and yet the Israelites killed many people. These were commandments, not prophesies, and the issue is not as simple as the cartoon critics make it out to be.
Third, D&C Section 114 says that it is "wisdom" that David W. Patten should settle up all his business "as soon as he possibly can" that he may perform a mission that following spring. However, David W. Patten died in a battle against a mob - Captain Bogart's "command" - while serving in the Caldwell County Militia. This revelation was not a prophecy, as far as I can tell, except perhaps to imply that it Patten's business was not settled up as soon as possible then he might not serve the mission. Patten was a good man, but he made a judgment call to charge against the mob - and he had to of known that his life was in danger when doing so. Do the anti-Mormons expect us to interpret Section 114 as saying, "David Patten is invincible and cannot die until he serves a mission next spring?" David Patten made what was in retrospect a bad judgment call. And the Lord knew he was going to make it, and provided him in advance with another option - to focus on a mission. Patten's death was tragic, but a lesson from which we can learn.
As knowledge shines forth in the Last Days, the Lord lights my path of faith with His Spirit.