How does reconstruction using video compare to using standard reconstruction using still images? What similarities and differences are there. Finally what can and cannot be reconstructed using standard stereo methods?
They are very similar, both would be considered Structure from Motion (SfM) algorithms. Both may use similar algorithms for matching features between images ie(feature descriptors, template matching or optical flow).
One of the major differences is that reconstruction from a video sequence would assume that the images are ordered while reconstruction from photographs may be unordered.
Here are projects and software packages to compare.
PfTrack vs ImageModeler vs Bundler
PfTrack calculates structure and motion from ordered images, the second from unordered images and requires the user to manually define matches, while the last is largely automatic and can take unordered images as input.
As for your last question, scale cannot be reconstructed from either method without adding a known object to the scene.
I hope this helps get you started.