Note that topolino (I can't spell or pronounce his full name!) deliberately left in the 'tap to focus' segments of the video, so that you can see the speed and parameters of the 808's lens mechanism focussing - a useful benchmark, and seemed fast enough to me.
From the video's description:
I have been privileged to use this magnificent camera phone. It has been a pure joy to shoot pictures and videos with it.
All videos shot using only Nokia 808 and tripod. NO macro lenses or other lenses used.
All video samples in this video are straight from the camera. I have not done any processing to the video but only pasted them together using Sony Vegas video editor. The audio is also separately recorded with Nokia 808 phone. I wanted to switch the original audio tracks because they were so noisy because of the wind.