I apologize in advance because I am commenting before reading all the replies in this thread. I hope I am not repeating topics that have been settled one way or another.
(1) WIND. I was about 25 miles from the site of this collapse on Saturday morning, and I can tell you it was QUITE windy at the time of the collapse. A picnic table umbrella went airborne and almost hit someone at our Farmers' Market. Our tent was straining at its stakes, and at times we held it down by hand to make sure it didn't go airborne, too.
(2) FIRST CRASH. The man who took the best video heard clanking, took a second or two to pull over and stop his car, saw the corner sagging, and started the video. That may have taken 5-10 seconds. Did parts of the crane break first?
(3) SIMILAR SCHEME? Regardless of how sketchy the rectangular tubing (and associate shoring) looks, it's almost always the case that engineers repeat the basic design scheme on buildings like this, spans, direction of metal slab ribs, slab thickness, and rebar ratio. Each building is a unique design, but they wouldn't change anything radical from one building to the next, and they would have checked for reasonable agreement with previous designs. They build them in one city after another. So, the question becomes, was anything significantly different with this design?
(4) DROUGHT. Finally, this is New Orleans, and the soils are notoriously soft and still settling. We have almost been in a drought here. We had 0.17" of rain in all of September, and no rain to speak of since then. Just note that in case the wind caused some sort of problem for the support of the crane. Did the water table drop? Doesn't seem likely to have an effect, based on the mode of failure, but any unusual conditions are something to think about.
The video link posted by dold shows the man on the scaffolding without blurring (that portion has been blurred in the current version of the collapse video taken from downriver Rampart St).