Mormons claim that there were several witnesses to God's revelation to Joseph Smith. In the Testimony of Three Witnesses and the Testimony of Eight Witnesses, there were several people who signed a document stating that they had seen the tables of gold from which Smith read. The eight-witness testimony states the following:

Be it known unto all nations, kindreds, tongues, and people, unto whom this work shall come: That Joseph Smith, Jun., the translator of this work, has shown unto us the plates of which hath been spoken, which have the appearance of gold; and as many of the leaves as the said Smith has translated we did handle with our hands; and we also saw the engravings thereon, all of which has the appearance of ancient work, and of curious workmanship. And this we bear record with words of soberness, that the said Smith has shown unto us, for we have seen and hefted, and know of a surety that the said Smith has got the plates of which we have spoken. And we give our names unto the world, to witness unto the world that which we have seen. And we lie not, God bearing witness of it.

By contrast, Muhammed was a prophet who received revelation from the angel Gabriel while praying in a cave. (Sorry for quoting Wikipedia.)

Islamic tradition holds that during one of his visits to Mount Hira, the angel Gabriel appeared to him in the year 610 and commanded Muhammad to recite verses which would later be included in the Quran.

Regarding your second question, I'm afraid I can't answer it with cited sources. Because it doesn't seem like too much of a stretch, I will venture to guess that Mormons would regard the authenticity of Joseph Smith's revelation as verifiable and Muhammed's as not verifiable. As to Muslims' defense of Muhammed's authority, I suspect at least some would point to the supernatural events attributed to Muhammed.

I'm not sure if this is normal procedure on Christianity.SE, but... disclaimer: I am not a Mormon or a Muslim.

One of the major differences between Islam and Mormonism is that Islam rejects the divinity of Jesus:

Qu'ran, Surah 5:17 YUSUFALI: In blasphemy indeed are those that say that Allah is Christ the son of Mary. Say: "Who then hath the least power against Allah, if His will were to destroy Christ the son of Mary, his mother, and all every - one that is on the earth? For to Allah belongeth the dominion of the heavens and the earth, and all that is between. He createth what He pleaseth. For Allah hath power over all things." PICKTHAL: They indeed have disbelieved who say: Lo! Allah is the Messiah, son of Mary. Say: Who then can do aught against Allah, if He had willed to destroy the Messiah son of Mary, and his mother and everyone on earth? Allah's is the Sovereignty of the heavens and the earth and all that is between them. He createth what He will. And Allah is Able to do all things. SHAKIR: Certainly they disbelieve who say: Surely, Allah-- He is the Messiah, son of Marium. Say: Who then could control anything as against Allah when He wished to destroy the Messiah son of Marium and his mother and all those on the earth? And Allah's is the kingdom of the heavens and the earth and what is between them; He creates what He pleases; and Allah has power over all things,

Whereas the Book of Mormon explicitly affirms it:

Book of Mormon, Title Page- And also to the convincing of the Jew and Gentile that Jesus is the Christ, the Eternal God, manifesting himself unto all nations—

LDS belief is in direct opposition to Islamic belief. Mormons violate the entire basis of Islam called Tawheed or the oneness of Allah. To Muslims, without the belief of the oneness and uniqueness of Allah you have fallen out of the scope of Islam and are Mushrik (associating partners with Allah.) Tawheed is the most fundamental belief in Islam. It is so fundamental that saying "ashadu an lailaha illallah" (I believe there is no god but Allah) upon death can save a man from the fire of hell and is narrated in various authentic hadith. It should be noted that if the dying man only says "ashadu an lailaha illallah," he is granted entrance to heaven as these sahih hadith state:

The Prophet(pbuh) said: "Whoever says: there is no god but Allah enters Paradise." Tabarani narrated it from Abu Dharr in the Kabir (7:55), Ibn Hibban in his Sahih (31), al-Hakim in his Mustadrak (4:251), al-Mundhiri in al-Targhib (2:422), al-Haythami in Majma' al-zawa'id (1:18), Ibn 'Adi (7:2639), Abu Nu'aym in the Hilya (7:174), and al-Bazzar from Umar'.

The Prophet(pbuh) said: "Whoever says there is no god but Allah enters Paradise even if he commits adultery and even if he steals (i.e. even if he commits great sins)." (Nasa'i, Tabarani and others from Abu al-Darda' - sahih).

It is important to note that Tawheed (the belief in the oneness and uniqueness of Allah) is so important that one need not bear witness that Mohammed is a messenger at all. Bearing witness that there is no god but Allah is sufficient.

Primary contrasting beliefs

Surat til-Iklas can serve as one of the bases for Islamic Tawheed:

1. Say, "He is Allah , [who is] One,
2. Allah, the Eternal Refuge.
3. He neither begets nor is born,
4. Nor is there to Him any equivalent."

As anyone who is informed of both Islamic and Mormon theology could see, Mormonism is the direct opposite of Islam as far as belief is concerned.

1. Mormons belief in the existence of other deities so their god can not be one.
2. Mormons end all their prayers with "In the name of Jesus Christ" so this Ayat is violated.
3. Mormons belief that God begets spirit children with his celestial wives and God was born of a man before he received exaltation.
4. Mormons believe as man is, God once was. As God is man may become. So there are an infinite number of gods like their god.

More notable differences

• Mormon women don't observe hijaab (covering for women) except a kind of wedding veil headdress in the temple.
• Mormon men don't have to be circumcised.
• Mormons have mixed services where shaking hands with men is actually required i.e. through the veil in the temple.
• Mormon women don't get a dowry.
• Mormons don't ritually slaughter animals.
• Mormons can wear bathing suits in public.
• Mormons eat pork.
• Most Muslims love coffee and tea and these are permissible acts.
• Mormons don't do Hajj.
• Mormons don't pray 5 times a day.
• Mormons don't make ablutions in order to pray.
• The typical Mormon fasts 12 days a year while Muslims fast over 30 days a year.
• Mormons keep meticulous records of their members both living dead while Muslims have no such custom.
• The LDS church is a kind of central corporation in Salt Lake City through which all meeting houses and the Mormons therein are controlled. Muslims have no such custom.
• Mormons meet socially with free mixing of women and men. Muslims frown on this type of behavior.
• The Mormon scriptures have no rhyming.
• Mormons have no rules for reciting scriptures such as Tajweed or Tarteel.
• Mormon prayer is unstructured and is similar to du'a (personal supplication) as such their prayer has no resemblance to salat (practice of ritualistic prayer) which has to be preformed a certain way to be accepted.
• Mormons can't have more than one wife while Muslim men can have four.
• Mormons routinely have pictures and statues of Jesus and prophets in their meeting houses or temples while you will never find this in a mosque or the house of any believer of Islam.
• Muslims believe there are 4 types of creatures created by Allah: the jinn (made of fire and unseen by man), the angels, mankind and animals. Mormons do not believe in the jinn.
• There is no continuing revelation in Islam. However, we do follow Fatwah (religious edicts) that are made by ijtihad (independent reasoning) and Qiyas (deductive analogy.) We have no scholars that are appointed by God.
• We do not believe that Jesus is divine but only a man.

Similarities

• Both Mohammed (pbuh) and Joseph Smith received revelation through an angel. 2. Both Mormons and Muslims are prohibited from gambling and drinking alcohol. 3. Both Mormons and Muslim place importance on moral behavior.

• We do believe Jesus was born of a virgin and the Messiah and will return in the last days.

Works Before Faith

• In Islam you can be a very moral and good person but are still an unbeliever and a Mushrik (associating partners with Allah). This is evidenced in Islamic history in the story of Abu Talib. Abu Talib (the uncle of Mohammed (pbuh), the father of Ali and the wife of Fatimah (daughter of the prophet (pbuh)) died without accepting Islam and clung to the beliefs of the Meccan polytheists. He was, however, a good and moral man and supported prophet Mohammed (pbuh). This is good evidence that your works will not save you and your faith and belief in Tawheed (Oneness and Uniqueness of Allah) is required to enter paradise.

The similarities are superficial. I think that it is apparent, by my answer to this question, that it is impossible for two religions to be similar that contradict each other so seamlessly on basic belief.

References

I have been a practicing Muslim for twenty years. I am studying Islam at Islamic Online University under Sheikh Bilaal Philips. I was briefly a member of the LDS Church for two years and I received temple endowments.

• http://www.ahya.org/tjonline/eng/02/1tawheed.html
• http://islamqa.info/en/49030
• https://www.lds.org/manual/gospel-principles/chapter-47-exaltation?lang=eng
• http://salaf-us-saalih.com/2011/01/03/the-difference-between-a-mushrik-and-a-kaafir-shaykh-albanee/
• http://www.islamicacademy.org/html/Articles/English/LA%20ILAHA%20ILLALLAH.htm