When you encounter and want to address vertex linking anomalies, the first step is to resize or reposition the envelope about the problem link. Most often, the culprit is an envelope having been created too small to surround, and thereby influence, certain vertices.
This can happen because your biped character misaligns slightly with the mesh, or the link lengths used to create envelopes with unbounded Bones systems links were insufficient to surround all vertices attached to the link.
Another potential source of problems is overlapping inner bounds. This can sometimes create too strong a deformation at the joint.
You'll note problems with vertices as you preview motion. It sometimes looks like vertices got left behind when the link they were supposed to be attached to moves in 3D space. In fact, that's just what is happening: they weren't assigned to any link at all, and remain where they were at the initial skeletal pose: the pose of the mesh and its skeleton at the time Physique was applied and initialized.
The other case would be vertices being moved too much, resulting in a dent in the mesh. This would be fixed by decreasing the overlap of the envelopes affecting a joint.
Stray vertices (above) reassigned to correct link(s) by modifying envelope shape (below)