<p>What are the best practices when managing a software project involving a non-English-speaking client?</p>

<p>What communication issues are relevant? Would you maintain documentation in both languages (especially updating the specifications regularly)?</p>

My native language is not English, so I'm on the other side. There were times when we had to write project documents in 4-6 languages.
Try to find somebody who understand English (like a key person). I try to avoid the communication in different languages on a project. Of course you can talk and write on different languages with project members, but if you talk or write to all members of the project at once, it should be one language.
Documentation should be maintained in as many languages as many involved. All documents should be updated on a regular basis and try to avoid the situation when you have to tell them that "the English is the current one". Find someone who is native in the target language and translate from English for you. It will be far more better, understandable, and more native than if you try the other way around.