Lets start off with this whole notion of Gringotts goblins somehow being about to destroy Horcruxes(You know, that very ancient, very evil, and very forbidden form of magic) by feeding it to pigs, somehow transferring the Horcrux soul to the pig, and then slaughtering the creature to destroy the Horcruxes. There's just a whole bunch of WTF involved in this whole process. Firstly, according to Harry and Hermione, Dumbledore refused to inform them of this easy method(that the author made up, mind you) because he was suddenly a Fantastic Racist who didn't consider methods by other races. This implies that Dumbledore knew of it from the start, which means Voldemort probably damn well knew of it in the original timeline as well. You'd think that Voldemort, upon discovering that his precious treasures could be so easily destroyed, would have sought out some other means of immortality lest someone, like Harry, discover this and use it against him. Failing that, you'd then think that Voldemort would go and, at the very least, slaughter every goblin within Gringotts and then destroy the institution himself as a means of keeping this particular method of Horcrux destruction from being discovered. At most, Voldemort would have probably committed out-and-out genocide(which would fit with his character) as a means of self-preservation. Secondly, even when Horcruxes were made out of animals(see: Nagini), it was still required to have something capable of destroying Horcruxes(like a Basilisk or the Sword of Gryffindor) in order to destroy the Horcrux! So how in the hell would roasting the pig alive do anything to destroy the Horcrux!?
The Crapsack World introduced (and left behind forever) in the first chapter. Aside from how unlikely it is that the people who suffered and lost loved ones under Voldemort's rule would just sit back and allow Umbridge to take power, the two pro-pureblood laws she introduces (or rather, the ones we hear about) are absurd. First, she states that it is legal for a pureblood to rape a Muggleborn or halfblood, and then specifies "The girls should be delighted to receive the attentions of such noble wizards" - so does this law account for a pureblood witch raping a Muggleborn wizard, or homosexual rape? Second, Umbridge has made it illegal for a halfblood or Muggleborn who gets pregnant by a pureblood to terminate her pregnancy - but isn't encouraging the production of halfbloods precisely the opposite of what she's supposed to be doing?