This is an excellent question, as any source you use will have strengths and limitations.

Primary sources, which are generally understood to be eyewitness accounts of an event or the original document in question (e.g., the novel Middlemarch rather than a book about Middlemarch), have a great deal of authority. A person who actually witnessed the bombing of Berlin can comment on the experience in way no one who was not there can replicate. Likewise, a quote from Middlemarch in support of a thesis most often has more authority than a quote by critic interpreting Middlemarch (since even the best critic can get details wrong).

At the same time, primary sources can be limiting because they lack the perspective that comes with a more detached view of an event. A person who comes out of an air-raid shelter to see a hotel and a block of cars in flames can give a very vivid and emotionally compelling account of what she sees, but she probably does not know how many planes flew on the raid that night and cannot know, while feeling this particular night is the end of the world, that a worse bombing will occur nine months later.

Therefore, secondary sources—secondhand accounts of an event that amass a group of primary sources and research into statistics and the drier aspects of an occurrence—are also very important. Especially when a good deal of time has passed since the event, they can make an event intelligible in a way primary sources cannot. Their problem is that they are derivative: an extra layer of consciousness is sifting through the evidence and providing a framework that may or may not be distorted.

No one source can offer both an up-close and emotional reaction to an event and a detached and analytic look from afar. That is why it is important to look at as many sources as possible when doing research, both primary and secondary. When possible, go back to primary sources, as secondary sources can and do get things wrong, but also use the secondary sources to give yourself a broader context for what you are researching.

Primary and secondary sources of data both have advantages and disadvantages.

Advantages of the secondary sources include:

• Ease of access because the work has been published and readily available. The internet has further made secondary sources easily accessible.
• Secondary sources have a low cost associated with access and use with some online libraries charging less than $10 to access.

Disadvantages of secondary sources include:

• The quality and reliability of the information cannot be easily guaranteed, and at times the information may be misleading.
• Information provided by a secondary source may be outdated.

Advantages of primary sources include:

• Primary sources may provide deeper information such as emotions, socioeconomic status of the source and other metrics that would otherwise be lost in a secondary source.
• A primary source is easily verifiable because one can query the same source.

Disadvantages of primary sources include:

• Primary sources are susceptible to bias and exaggeration.
• Access to primary sources may be expensive and time-consuming.

Any source, whether primary or secondary, will have both values and limitations.

To look for the limitations of the source, you need to look at what factors might make the source less valuable to you.  For example, if a source is written by a biased observer it might be limited because it presents only one side of a story.  If it is written by someone who is not an expert in that field (perhaps by a journalist rather than by a historian) it might not be as professionally researched as it should be.  These types of things would limit the usefulness of the source.

Conversely, some factors might make a source have more value for you.  For example, I recently read a book about the Battle of Midway written by Japanese naval officers.  If I were writing a paper about the Japanese mentality during WWII, this would be valuable to me because of who wrote it.  It might be valuable because it is written by a particularly well-known scholar using detailed and meticulous research.  To understand the value of a source, you have to see how closely connected it is to your topic and you have to evaluate it to see if its limitations are too serious to make it useful.