I've taken a look at the walk cycle animation and I think there needs to be a tween in between frame 3 and 4: the head snaps back into the same position as frame 1 while skipping the frame 2 tween (the same happens at the loop point, between frame 6 and 1).
For the run animation, you might need to introduce height changes like you did with the walk cycle as running follows pretty much the same rules as walking.