So, with that in mind, here is my straight-forward, but accurate take on the topic and I leave it you to draw your own conclusions. As always, the best place to start is with the Holy Quran. The concept of Muta, revolves around one main verse:
"(...Except the forbidden women) the rest are lawful unto you to seek them with gifts from your property (i.e., dowry), provided that you desire protection (from sin), not fornication. So for whatever you have had of pleasure (Istamta'tum) with them by the contract, give unto them their appointed wages as a duty. And there is no sin for you in what you both agree (in extending the contract) after fulfilling the (first) duty. Lo! Allah is ever Knower, Wise." (Surah 4, Verse 24)The word 'marriage' is specifically not mentioned in this verse, it is instead the word 'istamatatum' which translates to muta. It was a practice that was allowed during the time of the Prophet and according to many Sunni books was later prohibited by the second caliph, Umar. "The Verse of Hajj-at-Tamatu was revealed in Allah's Book, so we performed it with Allah's Apostle, and nothing was revealed in Qur'an to make it illegal, nor did the Prophet prohibit it till he died. But the man (who regarded it illegal) just expressed what his own mind suggested." (Sahih Bukhari, Book 60, Number 43). The man mentioned was Umar the second caliph.
Furthermore, in Sahih Muslim, the claim that Umar banned the act of Muta is confirmed in the following hadith: "Abu Nadra reported: While I was in the company of Jabir b. Abdullah, a person came to him and said that Ibn 'Abbas and Ibn Zubair differed on the two types of Mut'as (Tamattu' of Hajj 1846 and Tamattu' with women), whereupon Jabir said: We used to do these two during the lifetime of Allah's Messenger (may peace be upon him). Umar then forbade us to do them, and so we did not revert to them." (Sahih Muslim, Book 8, Number 3250) So, with the aid of Sunni sources, it seems as if Muta is allowed as according to the Quran, practiced during the time of the Prophet and was subsequently forbidden by the second Caliph. As a Muslim, I think it's important to follow the Prophet rather than the second Caliph, don't you?
Having tried to prove the authenticity of Muta, obviously it is a topic that raises much debate because of what it means. I don't want to get into the rights and wrongs of Muta. It was introduced at a time when fornication and prostitution was rife, it was used at a time when men went to war and would be separated from their wives for long periods. Like any other rule or act, it is open to abuse. By all means criticise those who abuse the laws of Islam, but to abuse the act and furthermore Shias for practicing the act in a correct manner, when it is clearly allowed by God and his Prophet is wrong.