Today was like the third time I had to scour Google, SDN, and the Sitecore forums looking for a solution to this problem. So I'm going to post the solution here and hopefully next time I will search my own blog first...
Let's say you need to do a Sitecore query such as this:
/sitecore/content/Home/News Section/*
Note the space in "News Section". This causes an error, but there is a solution! Surround the bit that has spaces with pound symbols. Like this:
/sitecore/content/Home/#News Section#/*
This poses the question - how do you escape the # symbol itself if you need to use it? I haven't been able to find that answer, but if you see it - let me know!