Russ: The Dictionary is certainly source to consider, when determining how a word is used in common parlance. However, as anyone with any science or technical background can verify, it is not an authoritative source for professional jargon.

So, if we are applying the common man's definitions, you are quite correct. However, since this is an Astronomy forum, I assumed we were talking in terms of the jargon of Astronomers. Astronomers have no formal definition of planet. It is a topic that is actually in hot debate in recent years with the discoveries on Titan and extra-solar planets, particularly the planets that roam free from any star.

I am not sure if there is a formal definition of "Moon", but my suspicion is that it is as nebulous as "planet". I will have to look it up.