It seems I should have done a few more minutes of research. I found my solution with the help of an answer to a similar question on these forumsan answer to a similar question on these forums: I have to take advantage of the ":prologue", and ":epilogue" parameters to properly handle the command's output, and change the collection option to "output":
#+begin_src sh :results output file raw :file dump.sql :prologue "2>/dev/null" :epilogue ":"
mysqldump -u root -h 0.0.0.0 -P 49321 -proot cf_dev sforum_contacts
#+end_src
I had no idea these options existed, and don't understand what they do exactly -- the prologue option seems akin to appending it's value to each command in your block, and I have no idea what the epilogue option does.