I am trying to use live view for stiles and hand holding in the same way I have used the D300 but the D7000 takes so long to focus and take the picture. The focus miss-focuses and some times it will not focus at all, I use spot focusing,in the same way I do on the D300, I have no problems with the D300 in this method and obtain good reesoults. I would have thought that the new D7000 would work in the same way, but it seems they have have not followed the same root, which is a pity as I find this function a useful tool in the right constance.
I haven't used any LiveView before I got my D7000 (I had a D70 before) - Generally I use the TTL viewfinder, which obviously has zero lag and I think in the case of the D7K, 100% view coverage. However, the few times that I have tried to use LiveView, it has generally been unsuccessful because I have been handholding it, and am still learning the camera! The autofocus is sooooo much more sophisticated and complex than my D70, it is easy to use an inappropriate mode. I think you probably just need to learn what modes work for you in your environment with the subject matter at hand. When using the TTL, it is easier to point and hold the camera steady at the target object. When hand holding with LiveView, I for one can't hold it steady - so the autofocus will keep moving. My videos have been rubbish too so far for the same reason. My fault - not the camera's.
There are two modes for Live View in the D300, the hand-holding mode and tripod mode. The hand-holding mode uses "phase detection" for AF, tripod mode uses "contrast detection". Phase detection is the way normal (without live view) AF works, and it is much faster than contrast detection. The D7000 only uses contrast detection for focusing in live view (there aren't both modes for LV), so it is slower.
I think most DSLR Live View users use it when on a tripod. The best method for viewing/focusing when hand-holding would be to use the viewfinder.
What lens do you have mounted on the camera? The Live View on the D300 has two focus modes: handheld mode and tripod mode. In handheld mode, the camera uses phase detect autofocus and in tripod mode it uses contrast detect autofocus. Phase detect autofocus can be faster than contrast detect.
The D7000 only uses contrast detect autofocus when in Live View. Additionally, many older third party lenses may not be compatible with the contrast detect focus system on the D7000. In many cases, those lenses can be upgraded by the manufacturer. I know Sigma has a number of lenses that require upgrade to focus properly with the D7000 Live View.
The combination of contrast detect autofocus and/or incompatible lenses could explain your issues.