While I don't necessarily disagree, in many cases the parents/coaches understanding of the laws is meaningless due to the highly subjective nature of the LOTG, particularly Law 12 (the laws are more suggestions than anything else). Parents/coaches/fans/players biggest "mistake" is expecting consistency in the application of LOTG. There is no mechanism in the LOTG that promotes consistency. In fact, the LOTG promote the opposite by giving the referee the broad discretion to use his/her opinion within the "framework" of the laws (as opposed to the application of the actual individual laws themselves). A ref can rationalize just about any call based on the concepts of "game management" or "trifling", terms that are no where to be found in the LOTG. Not saying that is wrong or right, that's just the nature of the beast. Most controversial calls are not a result of the misapplication or misunderstanding of the LOTG, but merely a difference of opinion. Every ref has their own idea of how LOTG should be applied and in what context.
Expecting consistency from the application of LOTG is a fools errand. I've quoted this a few times before, but this is what Clattenburg (considered a top ref by many) had to say about consistency:
"The best referees, he believes, make their decisions based on context and balance. This explains why there can never be "consistency" in the way football is refereed. It is the courage to apply the laws with empathy, says Clattenburg, that distinguishes top officials from those on the next rung on the ladder."