According to the folks who made the 2012 documentary "How to Survive a Plague", his "callousness...at the very epicenter of the AIDS crisis...failed," so many even as it ravaged thousands of gay men just like him. Koch was apparently gay but never admitted it publicly. The best we got, when once asked about his own sexuality, was the following: "My answer to questions on this subject is simply, 'Fuck off.' There have to be some private matters left."
He took that official secret to his grave when he passed away earlier today.
I came of age just after the worst of the AIDS crisis. But that terrible decade in 1980s remains in our collective memory. It's true that Koch could've done much, much more to help combat the disease in those early years, provided more help to those struggling to survive and help others fight the disease. It was an epic failure of leadership from somebody who should've known better.
Regardless, I hope he rests in peace. This clip below from the feature film 'Shortbus,' by director John Cameron Mitchell features an elderly male character who is clearly based on Koch. Not seen in this clip, the character introduces himself to the young man as a former "mayor" of New York City and proceeds to try to explain away his terrible record on the issue. It's quite moving and worth a watch (as is the entire movie if you haven't seen it yet.)