Some of these drawings may look anarchic but they still have to obey some general drawing principles in order to be effective.
One of the hardest concepts my artists have to learn is to make funny asymmetrical drawings - that still look like they are wrapped in flesh and stuffed with cartilage and teeth.
Many cartoonists have been conditioned to believe that construction consists of perfectly even, symmetrical circles and ovals - all arranged on a mathematical grid. So when they translate gutsy storyboard or animation drawings to layout or cleanups, they tend to even everything out and make the characters look like flat robots - or traced model sheets.
Hopefully these tips might help avoid that.
A REALLY IMPORTANT CONCEPT TO REMEMBER:
ARE ALL CONNECTED FORMS!
Your mouth smiles because the cheek squeezes and pulls it up. When it moves up it also can effect the bottom of the eye shapes. Almost everyone seems to have trouble grasping this. There should be a whole course in this in animation schools I think.