One of the central doctrines of Mormonism is that the Christian Church has gone through a universal apostasy. In other words Mormons believe that the church is so far removed from what the apostles and Christ taught that it really is no longer the church at all. It is because of this that Joseph Smith is believed to have brought the church back to where it should be.
If you’re ever talking with a Mormon about these issues there are a few things you can bring up to show that the church has clearly not gone under a full universal apostasy.
1. Accuracy of the Bible
Many Mormons will argue that one proof that the church went through a complete apostasy is that the scriptures have been changed over thousands of years, and so we can’t trust the scriptures that we have today. This couldn’t be further from the truth. If you simply ask them to give evidence of this fact, they won’t have any. The Dead Sea Scrolls was evidence the accuracy of the Bible that we have now because it predated about any other Old Testament Manuscript we had up to that time by about 1,00 years. When we compare what it to our modern Hebrew Bibles it is 99% identical to what we have now, the only errors being slips of the pen and spelling differences. With that well of copied text there is no reason to think the church had lost track of Christ’s original teaching. They had the Word itself to guide them.
2. Peter the Rock
In Matthew 16:18 Jesus says “I tell you that you are Peter, and on this rock I will build my church, and the gates of hell will not prevail against it” Jesus is saying here that hell will not defeat or destroy his church. If complete apostasy has happened this isn’t true. Mormons will argue two points here. First, that the rock Jesus is talking about is not Peter, but the statement Peter makes in the verse before, that Jesus is the Messiah. Second, that this is saying that Hell cannot prevent the church from ‘invading’ hell since it is mentioning gates.
The first objection doesn’t take into mind Peter’s name or why Jesus would mention Peter at the start of the verse. The context lets us know already he is talking to Peter so Jesus has no reason to say Peter’s name again.
So, why say “I tell you that you are Peter”? It’s quite simple. Peter’s name is rock or in the greek ‘Petros’ and the greek word ‘rock’ in the passage is the greek word ‘petra’. Jesus is making a clear connection. “You are the Rock (Peter) and on that rock I will build my church’
As for the second objection it just doesn’t think things through. If Hell has conquered the church altogether and there is no church left then clearly the gates of Hell have prevailed to keep the church out.
3. John the never-dying
In the Mormon Doctrine of the Covenants section 7 John asks God if he can have power over death so he may minister and evangelize till Jesus’ return. God grants this request and so Mormons believe John is still alive. If John is still alive then there has not been a complete apostasy because there would be a remnant of the church still around of at least John and anyone else who may be with him.
4. Church Fathers
Mormons also reference many church fathers or other church writings in which doctrines are being corrected or even whole congregations are being outcast from the church. To them, this must mean that the church has completely lost track of the original Gospel of Christ. There is one massive problem with this argument. It fails to realize that the people doing the correcting clearly have a correct view of the gospel, and so there is still a church that has not gone apostate.
5. Biblical Text
Finally, Mormons will point out, similar to the church fathers, that even in the New Testament epistles we see the apostles themselves correcting and condemning people. If the apostles were having so much trouble even then, it must mean that the whole church would eventually go apostate. The problem here is that it completely ignores and contradicts what what we discussed from Matthew 16:18. Furthermore, there is no scripture which ever prophesies that the entire church will go apostate. There is a huge difference between saying the church needs some correction here and there and that the whole church is completely lost.
Overall you should see a clear grasp of the reasons why unlike Mormons might wish you to believe the church we have now is the same church that was established by Jesus upon the rock of Peter.
BEARDED DISCIPLE 
Excellent points made except #2 is dead wrong. Christ didn’t build His church on any fallible person–Peter or Joseph Smith. The foundation (rock) of Christ’s church is built on Peter’s declaration that Jesus is the Christ. If Jesus’ exact words were “BINGO! Peter!” we may not have had the splits of 1054 & 1521.
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Well, I don’t accept that the Roman Catholic Church is necessarily the church built on Peter. I was discussing this with my Mom the other day, and she is with you on it. That being said I think there could be justification to agree with you there. But I am unsure.
Why does Jesus mention Peter’s name in the midst of that same sentence, which he is talking about a rock, which is Peter’s name? To me it seems that he is pointing out specifically that Peter is the Rock he is talking about.
Ultimately, of course the church rests on Jesus and not Peter so perhaps I am wrong there. But it still just seems a stretch that it is talking about Peter’s statement.
There is a play on words here–rock & Rock. [I’ve read some references that Jesus didn’t word-play but actually used the terms rock & Cephas..I’ll stick with the word play.] But keep in mind that even though Peter was an apostle and most solid in his thinking, he was a foundation of sand in Galatians 2:11-14 when he was condemned before all men present in Antioch. Christ laid the foundation of His church upon Himself–the solid rock–and not foolishly upon sand. As rock solid as Peter was, he was not the sure foundation to build the church and Peter knew that and placed all of his faith in the sureness of the Christ.