The Symbian Error
When Elop took over they had Symbian (ancient but selling well), Series 30 and 40 (selling in the billions but for very little profit) and the stalled development of MeeGo from the Maemo / Moblin merger mess.
I seem to remember that before Elop the plan was to move Symbian downmarket to replace a lot of the Series 40 devices with ultra-cheap smartphones and build up the top end with MeeGo. However, MeeGo was a bust and Nokia instead had to keep Symbian at the top end of the range where they kept polishing it just enough to be acceptable.
So, when Elop came in he made the very wise decision to kill MeeGo which was going exactly nowhere. But he also made the mistake of saying that they were going to phase out Symbian which had the effect of making the market collapse completely. It was the way that Symbian was treated (and not the Windows tie-up) that in my opinion was Elop's key error.
Had he stuck with the the plan and simply shifted Symbian downmarket then that might well have protected sales. Remember, Nokia ended up spending a lot of time pissing around adding smartphone-like features into Series 40 (e.g. Nokia Asha) when they already had those feature in Symbian. Yeah, the Asha range sold pretty well but it was completely and utterly pointless to develop *those* when Symbian could do the job much better.
Nokia's fall from grace started before Elop took over, and Nokia is hardly the only mobile firm to suffer such woes. Motorola and RIM/BlackBerry made pretty much the same errors.