Q:

When should I use "a discussion of" vs. "a discussion on" vs. "a discussion about"?

“A discussion of”, “a discussion on”, and “a discussion about”: When is each phrase used in preference to the other?
If context is important, I want to use it as a subheading on a piece of non-fiction.

A:

Oh lordy, another "there's a difference, but I can't quite put my finger on it" question. But I'm gonna try anyway. :)

A discussion about a topic — this implies that the discussion was just a conversation, really, and it might not have stayed strictly on-topic.
A discussion of a topic — this brings to mind a true discussion, going into all sorts of details of the topic (and only the topic).
A discussion on a topic — here I picture the discussion to be somewhat one-sided, almost a lecture.

Note that all of these connotations are vague and amorphous, and can be overridden by customary usages, or by what "sounds best" in a given context. If you pressed me to suggest a single best choice, today I'd go with "of". No guarantees about tomorrow.

A:

I suppose the answer depends on what your subject is, and what tone you're trying to set. 

"Discussion on" can sound serious or pretentious or formal, to me, as in:

A discussion on the subject of
  probity, wherein we discover an
  upstanding truth

"Discussion of" could describe the particulars of the event of the discussion (currently happening, perhaps having just happened), even separate from the explicit topic: 

A amusing discussion of whistles,
  plastic and otherwise

Or it can refer directly to the subject at hand, a summary of what you will discuss: 

A discussion of monsters, meteors, and
  meerschaum pipes

"Discussion about" sounds informal.  "Here's some stuff we're talking about." 

A discussion about some things which
  happened in the garden that Wednesday

