The problem that many have mentioned with regard to primary sources is that of perspective. That's why secondary sources (those who are experts in the field) are so important. We don't have to be the expert when using these sources, we simply have to be able to understand the interpretations that experts have deciphered. Then we have to form an opinion of those.

As others have stated primary sources are generally only form one point of view, however all research has the possibility of being biased. As you use and collect sources it is your responsibility to determine what is and what is not. I think that a combination of primary sources and secondary sources are good.

The historian, in order to properly interpret and understand primary documents, must acquire great volumes of information about every aspect of the times that produced the documents.  And as well, the historian must understand the use of the language at the time the document was written; even some of the same words will have different meanings a generation or a century later, and contextualized meanings can be very obscure.  A hugh investment of time and labor.

The student can choose a document that has already been analyzed and interpreted, and use that product along with his reading of the original document.

The professor may limit the student's use of resources for analysis and interpretation to what has been presented in the course so that the student's analysis and interpretation will be original work.  The student's product will therefore most likely be very shallow.

However that may be, the exercise will help the student to develop skills that may be useful later in analysizing and interpreting things that life or further scholarly study throws in the student's path.

It is important to remember that primary source documents are often our only source of information about the past. As has been pointed out in previous posts, they do not tell the whole story. Furthermore, we only have those sources which have survived. In Hidden History, Exploring our Secret Past, Daniel Boorstin points out that although many Puritan era sermons survive, few textbooks, etc. survive, simply because no one read the sermons whereas the textbooks were in constant use. The sermons survive, often in good shape; the textbooks were worn out and disposed of. This makes our view of the Puritan era somewhat skewed. In The Ghosts of Cannae, Robert O'Connell points out that it is impossible even to locate the battlefield where Hannibal destroyed the Roman army. 

 Then too, all sources have some degree of bias. The author of those sources spoke from a certain point of view. If he wrote for future generations, he placed his own interpretation on events.  We read/understand only that which he wishes for us to see and understand. The old adage that "history is written by the victors" is true, as is the expression that "the first casualty of war is truth."

By the same token, generalized history texts are not always reliable for the same reasons. Until very recently, Japanese textbooks scarcely mentioned Pearl Harbor. Similarly, little mention of the impact of the bombing of Hiroshima is made in U.S. textbooks; although the Japanese make great mention of it. Until very recently, the Southern U.S. received very little mention in textbook discussions of colonial America because most historians from the Civil War era deliberately downplayed the role of the South.

Having said all that, the very essence of the historian's craft is interpretation. He should be able to analyze the point of view of documents, and interpret them accordingly. Time and place should be considered.  Will we get it right all the time? Of course not. However, this is what keeps history exciting, and prevents it from becoming a boring recitation of meaningless facts and dates.

Another downside of working with primary source documents that I and my students deal with is that many of them were written or created centuries ago, and the language in the modern day is quite different.  This makes it that much more difficult to understand context or hidden meaning, given that many students (and myself included at times) struggle just to translate the basic meaning.  Old English from the American Colonial Period can be extremely difficult, especially from the 17th century, and often times personal letters or diaries from those who were not well educated leave you guessing whether or not a word was misspelled or has just fallen out of usage, or was considered slang for the time.

I like primary documents in that they are free of the filters that come with repeated interpretations (in textbooks, for example), but there are times when using them in class is either challenging or impractical.

The major problem with using primary sources is that they do not cover everything that you might need to cover in a course.  At least, they do not do it efficiently.  Look, for example, at the WWI propaganda posters that I have linked to.  If you look at them, you will know some things about WWI.  But there will be many things you do not know.  You will not know why the war started.  You will not know how the poster got made.  You will not know what sort of an impact they had.  This means that you end up with major gaps in your knowledge.

Or take the Emancipation Proclamation which is my other link.  If all you read is the primary source, you do not know anything about the context.  You do not know why Lincoln issued it when he did.  You do not know what his previous attitudes towards slavery had been.  You do not know that there were many slaves who were not freed by this (unless you already know about the border states, for example).  Again, gaps.

So primary sources are great to teach you about little parts of history.  But there is no way that you could learn all you need to know just by looking at primary sources.