There are many kinds of reference books available in Japan: specialized dictionaries (dictionaries of slang, idioms, phrasal verbs, and so on), and books that focus on particular aspects of grammar and usage. I haven't looked at most of these, and so I can recommend only a few.
If you have a reference book that is especially useful, please send me e-mail about it, and I'll post the information here. (I'd like recommendations from students and teachers of English only, so if you are a book company representative, please don't send me e-mail!)
The books below are ones that I have used in class or that I think can be especially helpful for Japanese students of English.
I used to use this as a required textbook in my freshman English classes at the School of Law because every student in the class makes some of these mistakes.
This book contrasts typical Japanese and English ways of presenting information, and it can help you understand why some sentences that are grammatical in English just don't sound natural in English. For example, in chapter 4, it explains why, in most situations, English speakers would say and write "There's a mouse in the kitchen" rather than "A mouse is in the kitchen."
The first part of this book describes mistakes commonly made by native English speakers when writing, and not all of it is useful for Japanese people writing in English. However, the second and third parts are very useful. They include sections on how to organize and edit essays and how to do research and document sources used in a paper.
This book gives many of the rules for using a and the, but of course, it doesn't cover all situations. It might be helpful for people who want to focus on learning how to use these words.