Common problems with literature reviews include:

List-like writing that lacks synthesis

(e.g. Smith (2003) investigated X and found Y. Jones (2000) looked at B and found C. Adams (1995) verified that M causes N. ...).

This is a bit like giving the reader one piece of a jigsaw puzzle at a time. Your job as a writer is to put all the "pieces of the jigsaw puzzle" together and then describe the resulting picture to the reader, pointing out what parts of the picture are clear, what parts are fuzzy, and what parts are missing altogether. You would then identify the goal of your research as being to bring one of the "fuzzy areas" into "sharper focus", to "fill in one of the holes", or to "develop the picture into new directions".

Not being sufficiently critical

Here it is important to note that the purpose of a literature review is not just to summarise what is currently known about a topic, but is also to provide a detailed justification for your research. That is, ultimately it is in the form of an argument, and this argument is developed by pointing out "holes" in the jigsaw puzzle that need filling or "fuzzy" parts that need clarifying see example 2. It might also put some disparate pieces together which suggest a promising line of research see example 3.

As research is supposed to make an "original" contribution to human knowledge, one of the things you need to do as a writer is to demonstrate that you are not simply repeating what has already been done before (or if you are, that there is a reason to have some doubt about the previous findings, perhaps as a result of some methodological weakness, thus necessitating the need for a confirmatory study with an improved methodology, or that the previous results are likely to need updating). Thus, as you review the existing literature, you need to identify any limitations, deficiencies, or gaps in existing knowledge or practice that need to be addressed. 

Not discriminating between relevant and irrelevant materials

A literature review is not supposed to simply demonstrate how much you've read, but provide a description of how certain parts of what you have read provide the foundation for, motivate, and frame your research. As such, the relevance to your thesis of what you review needs to be clear to the reader. With "background material", which is important for orientating the reader, it is particularly important to ask: "What of this background does the reader really need to appreciate what comes next, and what is ‘trivia' or unimportant detail which can be left out?" see example 5

Lack of a clear organisational structure

Using a mind map or plan can help to address this problem.

Exclusion of landmark studies

This suggests to the reader that the student "isn't on top of the field". But note, your literature review needs to be focussed on your thesis; examiners don't want to read material that is not relevant

Relying on material that is likely to be out-of-date

For PhD and MPhil students, note that the literature review that you did for confirmation will need to be updated for your final thesis.

Adopting a parochial perspective

This might happen if you were to mostly cite papers produced by the research group you are a member of or if you were to look mainly at the literature on a topic produced in one country or continent.