How can i make vertices that are along an edge but not part of it cut into the edge and do it for many vertices? https://webm.red/L9JA.webm

you can see the problem here through the webm and i want to fix it for the entire mesh and not just a few vertices.
You can use Degenerate Disolve function with all selected(a) in edit mode(Tab) for that. You can access it from the space search menu or from Mesh -> Clean Up -> Degenerate Disolve : 



It dissolves zero area faces and zero length edges.