Casino Royale is not just a great Bond movie but a great movie overall and historic one at that, as it rebooted the series. Bond started afresh with no relation to the continuity of the timeline of the series that had been running since 1962.
First things first - "The Amazing Spiderman" is not really the next in the series, Spiderman 4. This one is a reboot, this movie has got nothing to do with the timeline of the other three. This movie goes back again to the beginning -