One gotcha I ran into today I think is worth pointing out related to this problem: if the url for the ajax call is redirected then the header for content-type: 'multipart/form-data' can be lost.
For example, I was posting to http://server.com/context?param=x
In the network tab of Chrome I saw the correct multipart header for this request but then a 302 redirect to http://server.com/context/?param=x (note the slash after context)
During the redirect the multipart header was lost. Ensure requests are not being redirected if these solutions are not working for you.