Well, I think it's horrible.
(For a start, I hope the production is better than it sounds there, seems like there's some horrible radio compression going on.)
But even so, it doesn't seem like a great song for the following reasons:
1. The lyrics don't suit her London accent. The whole chorus rhymes with 'all', which she pronounces as 'aw'. As in 'let the sky faww, when it crumbuwwws, we will stand tawww or face it awww together'. It just doesn't sound right for a Bond song, considering most of the characters (Bond included) speak in a more... 'public school' British accent.
2. Quite frankly, I don't think she sang it very well, considering her talent. It starts really well, very Adele-like (particularly her melisma on the word 'overdue') but the way she hits the highest note each time in the chorus ('tall') is awful. I guess it's supposed to sound passionate by being slightly off pitch, but it comes across as lazy and inaccurate.
3. The backing 'let the sky fall' singers sound terrible. What were they thinking? The actual sound of them is nasty (although perhaps will improve at better quality), and the rhythm they've chosen doesn't seem to compliment the lead vocal in any way.
4. You know what, it's really just the chorus that's the problem. Even ignoring the three previous points, the chorus is simply not strong enough compared to the verses. The verses are good (maybe even great), the chorus is just bland bland bland. And even after the middle-8, the return to the chorus is very anticlimactic.
[edit] oh the iTunes version is out? I shall see if there are any much-needed improvements.
