The following remarks and questions on problem statements form a rather loose and unstructured collection. The are phrased in a seemingly silly and even caricatural style. But trust me: you don't want to know the percentage of students who frame problem statements that would not stand one or more of the following challenges. And trust me: I learned the hard way.
What is your 'unit of analysis'? If you want to know something about apples, then make sure that your question is about apples (and not about, say, fruit), and that your method reveals something about apples (and not something about, say, motorcycles).
Is your question normative or descriptive. If you want to know more about the historical decline of clogs as common rural footwear, don't ask whether the clog is ugly or not. (Apart from ethics and some other branches of philosophy, and some types of sociology, most sciences have a preference for descriptive questions.) You may be inspired to ask a descriptive question from a normative engagement, but that should be clearly distinguished from the question itself.
Is your question quantitative or qualitative? Contrary to widespread belief, knowledge is not always better when it is quantitatively expressed - i.e. statistically or mathematically sound. Sure, in many professions and sciences like economics, physics and construction engineering, you want to be sure that the numbers are correct. But in anthropology, ethnography, philosophy, and large parts of sociology, it is not the numbers that count. Some sciences are about stories, mechanisms, or in general: phenomena that are better described by words than by numbers. Don't try to measure things that are immeasurable. And beware that even one single observation can be scientifically valid and useful, if properly described. The world is more than means and standard deviations.
Don't ask 'what is' questions. They usually generate uninteresting results. The problem is that these
questions themselves do not distinguish between concepts and conceptions. They are likely to produce results that are uncontroversial, and therefore little revealing. A slightly better chance of getting interesting results obtains when you add 'according to': if you investigate what something is, according to a specific author who wants to solve a specific problem in a specific situation, you might be able to reveal something interesting. You may for example be able to explain why the meaning the author attributes to a concept, is not quite appropriate for a nearly-but-not-exactly-the-same problem you are facing.
Try thinking backwards. First, make up the most exciting or surprising thing you expect or hope to learn from your research. Then wonder whether this answer is really 'invited' by your research question.
For each word in your problem statement, wonder whether (1) it is a concept. if so, (2) whether the concept knows different conceptions within the whole context of research (=you, your research subjects, your peer-audience, etc), and if so (3) whether you have sufficiently specified and split-up the concept into elements that make it more unequivocal. In particular, the elements of the concept must be such that they clearly relate to the research methods and what they probe. (This need not be done inside the research problem statement itself, but certainly in its context and certainly univocally between members of your research team.)
For all questions (research questions, interview questions, questions of reflection), do the litmus test: pose them, either for real or in imagination, to someone as far as possible removed from your research and professional knowledge: your grandmother, your neighbour, a factory worker, the hairdresser, etc. If their answer makes no sense, then probably your question is either too abstract, its relation to your research topic underdeveloped, it may be ambiguous, or a combination of these and other characteristics of bad questions.