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.
I've been kind of dissatisfied with the head motion for the walk cycle and will probably try to fiddle around with that some more in the future. One thing I've considered was some kind of elliptical motion that might make it look a bit more stable.
I do kind of like the run cycle without the height change though.