Well, the wife and I went to see "War of the Worlds" last night, and afterwards I stopped by the Tyler Barnes & Noble and bought the YBSF No. 22. I'm happy as the proverbial pig in poop. FOUR honorable mentions!
I had already heard on the Asimov's board that Bewildering Stories got its first HM, and I was the culprit. As I suspected, the honoree from Bewildering Stories was "I Got You", which ran in two parts in May 2004.
I also had two stories at RevolutionSF, "Pen Pal" and "The Rocket-Powered Cat", earn the honor and a short at Astounding Stories, "Circe in Vitro".
As to criteria I've heard, the best information I've had from people who would know is that an HM indicates GD read the story over and thought it was good - not great, or else it would be in the anthology.
I know Gardner doesn't give HMs to every story he reads, because last year I sent him a magazine which had a story of mine. He mentioned me in the acknowledgements this year, I assume because I sent him the mag, but he didn't mention the magazine or my story - no neither impressed him.