It was definately 7/23/85 and not the 24th. This is my confirmation..from the second issue of AmigaWorld:
"Imagine yourself at Lincoln Center, New York City, in formal dress. You are standing
amidst a sea of tuxedos and evening dresses. No, you are not attending a ballet at the New York City Theatre or an opera at the Met You are attending theworld premiere of Amiga at the Vivian Beaumont Theatre.
On July 23, 1985. the Amiga personal computer premiered
with a stellar performance to an audience of press, software and
hardware developers. Commodore shareholders, members of
the investment community, computer dealers and celebrity
followers. The star of the evening was the new Amiga itself.
which gave a dazzling display of its capabilities."