I do a bit of video on my Nikon D7000, mainly with the Tokina 10-17mm. The Tokina is very forgiving with focusing especially if you shooting in at 10mm. I leave the AF on AF-S and what I do is focus through the viewfinder first and then turn on liveview for the video. Trying to use AF through liveview will make it hunt and it bascially isnt worth bothering with.
Here is a video I knocked up with the Tokina 10-17mm and the D7000 using the same method........(watch in HD so you can see how sharp it is)