While the actual decision was definitely agreed with the board, I'm sure that the famous "burning platform" memo pressured them. I think that the biggest problem was his certainty that he knew what was wrong and was sure how to fix it.
Elop should have been fired, and probably sued, as soon as he published that memo; even if he was convinced that Nokia's products were crap, he should have kept that information to himself and Nokia's "inner" circle, because that's the only thing they had at that moment; after they had a new, shiny product out there, feel free to talk about how bad the old product was and how great the new product is, but his actions have no rational explanation. Even someone as passionate and perfectionist as Steve Jobs tried his best to sell products he considered sub-par, like the Mac OS in the first iMacs.
The decision to go for an unproven platform like Windows Mobile was a bold, extremely risky move, which is why Microsoft had to pay that kind of money to have Nokia use it exclusively. For me, the biggest mistake wasn't to use Windows Mobile, but to put all of their chips into it, after completely dismissing their own products. They could have kept developing their own products, and also Windows Phone and Android devices, and let the market decide. I'm convinced that the Android phone would have sold a lot better than it's Windows counterpart, and Nokia would have had their own OS out there to compare.
Now it may be too late for Nokia to react; not only because of time and money, but because of the dismissal of the engineering teams that took care of Nokia's new software developments (specially the Linux-based Series 40 platform successor Meltemi), the damage to the Nokia brand, and the dependency of Nokia to a soon-to-be-competitor like Microsoft, when they release their rumored Surface phone. It looks like they're betting everything on Windows Mobile 8, and it will probably work as well as it did with 7.
In my opinion, the best thing Nokia can do is to find some kind of credit line that can sustain them for a few more years, negotiate the removal of the exclusivity clause with Microsoft, and add some Android phones in their portfolio, to try to recover some of the market share that went to Samsung; then, invest as much as possible in the development of what works (the only good news lately come from the success of the Asha line), and make the only thing that can distinguish Nokia from the other vendors: innovate, innovate more, and then some!
Things like the PureView are a good example of the innovation that may help them survive, but only if they don't keep screwing up in the marketing department, like when they mentioned in the announcement that the megapixels were interpolated (which wasn't true), or using the "PureView" name for different things (for image stabilization or large number of megapixels).