How can I help my master's student improve his English communication skills?

As a writing tutor in one of the aforementioned university writing labs, I can say that the issues you mention are both incredibly common and absolutely fixable. It's amazing how fast the ESL students improve once given good one-on-one feedback with a focus on patterns of errors. The progress that the ESL students exhibited made the poor performance of many native speakers even more unbearable. It really goes to show that you can certainly help someone learn a new language, but you can't fix stupid.

Seconding k8t, charmcityblues. Writing centers are great resources and I refer students to them all the time. Depending on the students' personalities, though, I find it important to emphasize that going to the writing center is not a "remedial" thing but rather a useful part of the writing process. When I refer them to my institution's writing center, I often tell students that I occasionally make use of their services as well (which is true); that can help make them less reluctant to go themselves.

There are different sorts of problems in your list and so the students need different sorts of solutions. #1 for example is not only a non-native speaker issue. It's the sort of feedback that many native speakers also need, and is about writing style and audience. #2, 3 and 4 are definitely ESL issues, but are really quite hard to fix. Not only does the student need to read about correct usage, but also just needs to read a lot of writing IN correct English to get a good sense of idiom, article usage, etc. Recommend that they read more journal papers written by others, which they should be doing anyway. #5-8 are really easily solvable. The student just needs to be told what not to do ("don't put multiple spaces in a sentence", or "this is how verb agreement in English works") and then told to use searches or auto-correction to find errors in the future. A search and replace for double spaces, would solve #7. And even crappy grammar correction software like the inbuilt one in MS Word will get verb agreement and capitalisation right more often than not.

It doesn't sound like they need a book about why things like antecedents need pronouns. It sounds like they need English as a Second Language lessons.

When I taught composition in China I used to talk to students about how they were taught to organize essays - I was getting tons of essays that seemed to me thesis-less and full of weird platitudes and all wrong in the same way, but once I understood how they had been taught to structure essays, I was able to target my writing advice much better. "You learned that you conclude your essay like X; in US English we are taught to conclude our essay like Y", for example. I also wrote several really simple short essays with notes and handed them out as models. I did short, targeted lessons on easy-to-fix problems like verb agreement and capitalization. The idiomatic language thing I only fixed by feedback on individual papers, because each instance was different - although if I saw something across multiple papers I might bring it up in class. Gosh, I miss teaching composition in China.

Surely your university offers ESL classes. Can you suggest that your students take these lessons?

Good ideas. I used to use my institution's writing center as an undergrad so I think they are pretty great. Unfortunately this student is actually visiting from another institution so he doesn't have access to the same resources that an enrolled student would have.

I work for a company where native speaking PhDs edit pre-publication manuscripts for non-native speakers. All of the things you're discussing are really common, and we get paid to solve those problems and make the articles read like they were written by a native speaker. Your school's writing center may definitely help, but it may be that ultimately the best thing for your student to do is to work with you (or their advisors, etc.) to get the content as well done as possible and then to pay somebody like me to edit their final copy. I hope that many of our clients look at the changes made to the final version and learn things, but, for example, idioms are very hard for non-native speakers of any language to ever get comfortable using fluently.

Incorrect use of definite and indefinite articles This one is not a good hill to die on. I spent a year teaching ESL to people whose native language doesn't have articles, and no matter how good their general English was they just couldn't get this one right consistently. It's funny that "a"/"the" confusion is a mistake that native speakers almost never make, no matter how terrible their grammar is in every other way.