Is The Muwatta of Imam Malik Authentic?
Question

How many hadiths are there in the Muwatta of Imam Malik?
Praise be to Allah.This is a brief introduction of the book entitled Muwatta al-Imam Malik; we ask Allah to benefit us thereby. 
Status of the Muwatta of Imam Malik
Al-Muwatta is one of the great books of Islam which includes a number of marfu’ hadiths and mawquf reports from the Companions, the Successors and those who came after them. It also includes many rulings and fatwas of the author. 
The Muwatta is so called because its author made it easy (watta-a) for the people in the sense that he made it easily accessible to them. 
Imam Malik said: “I showed this book of mine to seventy of the jurists of Madinah, and all of them agreed with me (wata-ani) on it, so I called it al-Muwatta.” 
Why was the Muwatta compiled?
The reason why it was compiled: Ibn ‘Abd al-Barr (may Allah have mercy on him) stated in al-Istidhkar (1/168) that Abu Ja’far al-Mansur said to Imam Malik: “O Malik, make a book for the people that I can make them follow, for there is no one today who is more knowledgeable than you.” Imam Malik responded to his request, but he refused to force all the people to adhere to it.”
The number of transmissions in the Muwatta
 Imam Malik read the Muwatta to people for forty years, adding to it, taking away from it and improving it. So his students heard it from him or read it to him during that time. So the reports in al-Muwatta are many and varied because of what the Imam did of editing his book. Some of his students narrated from him before it was edited, some during the process, and some at the end of his life. Some of them transmitted it in full whilst others narrated part of it. So a number of transmissions of the Muwatta became well known, the most important of which are: 

The transmission of Yahya ibn Yahya al-Masmudi al-Laythi (234 AH). This is the most famous transmission from Imam Malik, and most of the scholars based their commentaries on it. 
The transmission of Abu Mus’ab al-Zuhri, which is distinguished by the additions contained therein. It is the last version transmitted from Malik and it is still in circulation among the scholars. 
The transmission of ‘Abd-Allah ibn Maslamah al-Qa’nabi (221 AH). This is the largest version of the Muwatta, and ‘Abd-Allah is one of the soundest of people with regard to the Muwatta, according to Ibn Ma’in, al-Nasai and Ibn al-Madini. 
The transmission of Muhammad ibn al-Hasan al-Shaybani. 
The transmission of ‘Abd-Allah ibn Salamah al-Fahri al-Masri. 

And there are many others. Shaykh Muhammad Fuad ‘Abd al-Baqi (may Allah have mercy on him) spoke about the narrators of the Muwatta and discussed fourteen versions of it, in his introduction to the edition of the Muwatta that he edited (pp. 6-16). 
These versions differ in the order of the books and chapters, and in the number of marfu’, mursal, and mawquf hadiths. The wording of the hadiths also differs greatly. 
How many hadiths in the Muwatta
The number of hadiths in the Muwatta differs from one version to another, and according to the system of numbering. That is because some scholars counted every report from the Companions or Successors as a separate hadith, whilst others did not count them in their numbering. Hence it is sufficient for us to mention the numbers that are mentioned in some of the edited versions of the Muwatta, which are: 
The version transmitted by Yahya al-Laythi (which is the most famous version, and this is what is usually meant by al-Muwatta): It was numbered by Shaykh Khalil Shiha, and the number of hadiths that he counted was 1942, including both marfu’ and mawquf reports. 
The version transmitted by Abu Mus’ab al-Zuhri was numbered in the edition published by the Musasat al-Risalah. The number of hadith in this edition is 3069, which includes everything, even the words of Imam Malik, hence the number is greater. 
Is the Muwatta Of Imam Malik authentic?
The conditions he followed in his book are among the most reliable and strongest of conditions. He followed a method of erring on the side of caution and choosing only sound reports. 
Al-Shafi`i (may Allah have mercy on him) said: There is nothing on earth after the Book of Allah that is more correct than the Muwatta of Malik ibn Anas. 
It was narrated that al-Rabi’ said: I heard al-Shafi`i say: If Malik was uncertain about a hadith he would reject it altogether.  
Sufyan ibn ‘Uyaynah said: May Allah have mercy on Malik, how strict he was in his evaluation of men (narrators of hadith). (Al-Istidhkar, 1/166); al-Tamhid, 1/68) 
Hence you will find that many of the isnads of Malik are of the highest standard of sahih. Because of this, the two Shaykhs al-Bukhari and Muslim narrated most of his hadiths in their books. 
Note: Imam al-Shafi`i made the comment quoted above before al-Bukhari and Muslim wrote their books, as was noted by al-Hafiz Ibn Kathir (may Allah have mercy on him) in his summary of ‘Ulum al-Hadith (pp. 24-25). 
Method of the compilation of the Muwatta
In compiling his book, Malik followed the method of compilation that was current during his time, so he mixed the hadiths with the words of the Companions and Successors and fiqhi opinions. The reports of the Companions number 613 and the reports of the Successors number 285. 
In one chapter the marfu’ hadiths appear first, and are followed by the reports of the Companions and Successors, and sometimes he mentions the actions of the people of Madinah, so his book is a book of fiqh and hadith at the same time, it is not just a book of reports only. Hence you will find that some chapters have no reports, rather they contain the views of the fuqaha/jurists and the actions and ijtihad of the people of Madinah. An example of that is the chapter on produce on which no zakah is due, and the chapter on the fast of one who kills another by mistake, and so on. 
We also find that it is limited to sections on fiqh, etiquette and the actions of day and night. There is nothing in his book about Tawhid, zuhd (asceticism), the Resurrection, stories and tafsir. 
References:

Al-Fikr al-Manhaji ‘inda al-Muhaddithin by Dr Humam Sa’id, p. 111-118; 
Manahij al-Muhaddithin by Dr Yasir al-Shimali , p. 285ff; 
Muqaddimah Tahqiq al-Muwatta, ed. Fuad ‘Abd al-Baqi. 

For more about hadith, please see these answers: 197164 , 240606 , 85048 , 119516 , 239540 and 115125 .
And Allah knows best.