Relief, but I find the way his death is being celebrated in some areas rather distasteful.
Agreed. But then, there is a bit of a "Ding-dong, the witch is dead!" feel to the moment.
... and really, I can't blame New Yorkers, in particular.
Calling bullshit that he died in the firefight though. Shot in the head at point blank range to avoid any kind of trial, no doubt.
Maybe. Some more details have been coming out; seems a woman died trying to shield him, which seems to imply that 1) the firefight was maybe not so much a "fight" at that point, but 2) there was space between ObL and the shooter. Also, the mission was apparently a "kill mission"-- they were to take ObL alive only if he unambiguously surrendered. Otherwise, they were to shoot to kill.
So: looks like it was pretty much assassination with an "out" clause to avoid the risk of, say, an unnoticed webcam with a satellite feed or something broadcasting U.S. troops executing a prisoner in cold blood. "Unless the scene would work as an Al Qaeda recruiting tool, kill 'im."
In any case, it seems there were a couple survivors, so it's probably not just going to be a team of SEALS sharing some deep dark secret. And you can be sure there will be people trying to write books about this; we'll likely see the story poked and prodded from every possible angle by the time it's over.