There are all sorts of pitfalls that might lead to a poorly written problem statement. The most common of these, I would argue, is a failure to adequately think the proposal through. This leads to a sloppy or vague problem statement that will not be likely to convince anyone of the value of your research.
For example, poor problem statements sometimes fail to clearly define a problem. Instead, they talk vaguely about broad issues. This leads to a problem statement that is not specific enough to be useful.
Another potential problem has more to do with the style of the statement than with its content. This problem is the excessive use of jargon. People writing problem statements sometimes want to show just how much they know about the topic at hand and to show how professional and academic they are. Because of this, they produce dense, jargon-laden statements that fail to convey the real-world importance of the problem.