There are three main reasons for the disorder already occurring by the end of Act I. The first and most obvious is Lear's madness. He certain seems to be loosing it a bit, and his crazed banishment of Cordelia and Kent couldn't possibly have done anything but harm to him. The second reason is Cordelia's sister's treachery. It could be argued that they appear to be trying to protect him and their people by taking away his knights, he is crazy after all, if it weren't for Cordelia's parting words to them; "I know you what you are;/And, like a sister, am most loth to call/Your faults as they are nam'd. Love well our father:/To your professed bosoms I commit him:/But yet, alas, stood I within his grace, I would prefer him to a better place." And a few lines later; "Time shall unfold what plighted cunning/Who cover faults, at last shame them derides." These lines seem to indicate that Cordelia knows that Goneril and Regan are not only flattering Lear for gain, but also that they hold him in contempt, and will likely do him harm, and revealing the second harbinger of disorder.
The third indicator of the chaos to come is Edmund. I feel bad for him, for the contempt others hold him in because of the doings of his parents, but he quickly does what he can to dispel my pity for him with his evil attitudes as he works to turn his father and brother against one another. I find it ironic that he distains his father's belief in fate through astrology, yet confesses that because of when he was born he was supposed to be 'rough and lecherous,' yet doesn't believe himself to have those traits he was just showing.
Shakespeare's purpose in showing this disorder seems to come from the idea of dividing his kingdom. A divided kingdom would often lead to civil war and chaos, so Lear's deliberate dividing of the kingdom would probably have been viewed as deliberately inviting disorder.
Power in England was structured in a pyramid. The king on top, and wealth and power went to a few nobles who had all the money. Lear was trying to disrupt that structure in a way that would have alarmed the people watching the play. Cordelia took a great risk in not bowing to her father's wishes, as his denying her dowry could have driven away both her suitors, leaving her alone and destitute in a world that didn't favor lone women. In her case, however Cordelia's suitor from France still marries her, which would be very unusual since she had no dowry, and she wouldn't gain him an alliance with England.
Family dynamics can change depending on the health of a person, as others may come into their lives and as children grow up. Cordelia was Lear's favorite child, yet when she would not lie to him with flattery, he cast her off. Why? Did he not realize that her impending marriage would change is relationship with her? She would still love him, of course, but even with the play being in pre-Christian era, the belief would probably have been that the wife's foremost alliegence should be to her husband, and Lear should have understood this. In fact, it seems strange that he would have even questioned this part of the structure of society at all.
No one has a perfect family. This is shown in Edgar and Edmund's family. Gloster (or Gloucester as some versions call him) may have been unfaithful to his wife, it's never stated whether she was alive at the time of Edmund's conception. If Gloster was unfaithful to his wife than he was dishonest and breaking one of the oldest understandings of marriage. If Edgar's mother had already died, that Gloster was not responsible enough to remarry, and to marry Edmund's mother, or at least admit himself Edmund's father when the boy was a child, instead of waiting until Edmund was old enough to distinguish himself, and in doing so, add to Gloster's reputation. It seems very unfair that Edmund, and almost any other illigitmate child born until the the late 1900s should be punished for something that their parents did. Yet neither should Edmund take out his misfortunes on his brother, who was, in all probability, guiltless in tormenting him. After all, Edgar trusts Edmund completely, which does not seem like an attitude he would hold had he tormented Edmund before. I think that Gloster could have stopped his fate had he treated Edmund with kindness from the beginning of his life, rather than waiting until Edmund could add to his reputation to acknowledge him.
I don't actually seem him mocking Edmund, so much as simply being ashamed of his illegitimacy because it was Gloster's own act that was the cause of Edmund's bastardy. As Gloster was speaking to Kent, he was very frank about the manner of Edmund's conception, to the point that we would say he was being rude to Edmund, but really, for the time, the fact that he had acknowledged Edmund as his son at all was better than many bastards would have gotten. For this reason I think that more than anything it was the fact that he took so long to acknowledge Edmund, that led to Edmund's bitterness and Gloster's downfall.
(This review is patched up from posts I made on an online Shakespeare class)