Synthesized answer
The provided passages do not explicitly list the unanswered questions in "The Problems of Philosophy." However, Bertrand Russell states that he has confined himself to problems about which he thought it possible to say something positive and constructive [1]. For this reason, the theory of knowledge occupies a larger space than metaphysics in the volume, and some topics much discussed by philosophers are treated very briefly, if at all [1].
Therefore, while the passages indicate the author's focus and the areas he chose to address constructively, they do not detail the specific questions that remain unanswered by the book.
Synthesized from the book passages below. Chat with the book on Feynman for follow-up.
From the book
Title: The Problems of Philosophy by Bertrand Russell Description: In the following pages I have confined myself in the main to those problems of philosophy in regard to which I thought it possible to say something positive and constructive, since merely negative criticism seemed out of place. For this reason, theory of knowledge occupies a larger space than metaphysics in the present volume, and some topics much discussed by philosophers are treated very briefly, if at all.