cholling, further to what @kona has said, I checked the Canvas Guides -- How do I filter Conversations? -- and see that according to the screenshot there the search box defaults to "Search by user" (although that message doesn't appear in the search window of my own live Inbox).
So I tested what you described in Chrome (44.0.2403.157 m) by searching for a word I could actually see in one of the conversations, and the spinner spins for a few moments, after which I get the response "no results." However, when I entered a name, the spinner did its thing and then that name appeared in the dropdown; clicking on the name revealed all of the conversations involving that user.
There was a feature idea surrounding the ability to search the inbox by keyword or something other than user or course, but it's been archived due to lack of interest: If you feel you can develop a strong use case for this, you might want to resubmit it.
Or did I completely misunderstand what's going on? Are you in fact entering a user name and encountering the errors you described?
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