I've been trying to create a rig for my dragon character and I'm doing weight painting right now. However, some strange anomalies keep getting on my way.
Looking at the gif, at least two other bones are moving when you move that shin bone. The most likely explanation for your issue is that you have parts of the other leg weighted to one of these bones.
Edit: Another thing you could try is to set the armature modifier to deform the edit mode mesh, pose it so you get the deformed mesh and enter edit mode. From there, select one or the deformed verts and open the right hand panel in the 3d view ('N' panel). One of the sections there lists all the vertex groups and their weights that apply to that vertex. This should help you track down where the problematic weighting is coming from.