A tough one - I'd be interested to see other panelists weigh in!
The first thing to say is that it's hard to identify any limits to the subject matter of philosophical questions. Traditionally, philosophy has addressed questions about human nature, the nature of reality, knowledge, value, beauty, reason, and so on. But in recent decades, philosophers have turned their attention to an ever-widening circle of topics: medicine, law, the family, race, sports, business, gender, technology, religion the environment, and so on. So it doesn't seem as if the defining characteristic of a philosophical question is what it asks about.
One characteristic of a philosophical question is that it tends to be general. This is not to deny that we are often motivated to ask philosophical questions by very specific concerns. We might be motivated to ask the philosophical question 'what makes a person morally responsible for our actions?' by our interest in whether Charles Manson was responsible for his criminal actions. Or we might be motivated to ask the philosophical question 'what is the nature of causation?' by our interest in what causes cancer. But a philosophical question nearly always addresses a class of phenomenon rather than a single member of that class.
A second feature of many philosophical questions is that progress on them often requires analysis of, or investigation into, the concepts found in the question. 'Does God exist?', for instance, is a question for which we need to have some understanding of what 'God' refers to before we can coherently investigate the question. Suppose someone held up his pet turtle, which he happened to have named 'God', and claimed that he's thereby proven that God exists. This wouldn't be a satisfactory 'proof' of God's existence because the turtle lacks the attributes of 'God' referred to in the question (attributes like having supernatural powers, etc.) Likewise, 'is honesty a virtue?' or 'what is the value of knowledge?' are questions where, if we can answer them at all, we first need to arrive at some understanding of exactly what we're being asked.
Finally, philosophical questions tend to be such that either they cannot be answered by straightforward empirical methods (or it is controversial whether they can be answered by straightforward empirical methods). Logic, for example, is not an empirical science: Conclusions about which kinds of claims are entailed by other kinds of claims are not reached by conducting experiments, making observations, formulating theories, etc. Many moral philosophers would say the same about the fundamental claims of morality. Very often though, philosophical disputes revolve about whether a question can be answered through straightforward empirical means or not. For instance, 'what is the nature of consciousness?' is a philosophical question in part because some philosophers believe it can be answered through empirical investigations (in psychology, neuroscience, etc.), whereas other philosophers deny that it can be answered through those kinds of investigations. But the fact that there's dispute about the applicability of empirical methods in answering this question is a good indicator of the question's being philosophical in nature.