Thanks for your help so far!
To be more specific:

• How much data would get written out? If you have too much data written to the log, your disk space could fill up. I'm not worried about disk space... although I suppose it would be trivial to have it check for abuse of that kind
  Each new entry (appendage?) would be about 1k at most, methinks.
• What do you plan to do with the log? Who will see it and how?
  The form is basically just a registration form. It will take in name, email address, as well as a few items from checkboxes and radioboxes. This information need only be seen by myself and the system admins, although I'm not worried about preventing others from seeing it.
• If you plan to have an HTML log and serve it directly, you could have issues with SSIs (though I think it's unlikely you would do this).
  Uh... while I don't entirely understand that, I'm inclined to agree
• What data is stored there? Is it sensitive?
  As above, names, email addresses, etc. Not sensitive.
• Your users can't specify the log filename, can they?
  That's not needed... unless you think there's a benefit?

Basically,the file will hopefully look something like this:

**************************
Person #1
Name: John Doe
Email: Johndoe@hotmail.com
Entry3: This is some value
**************************
Person #2
Name: Jane Doe
Email: wifeofjoe@hotmail.com
Entry3: Blah blah... blah?
***************************
[download]

You get the idea. Thanks again for any help you can offer!