It was simply the use of cat hair instead of human hair.
As Professor Snape says to his class, potion-making is a subtle science and exact art. Changing even a little thing can cause the effects of a potion to differ drastically from the intended or usual effect. Polyjuice Potion is already a difficult to brew potion, and presumably brewing it is as much as if not more of an exact science as brewing more simple potions. Adding hair from a cat instead of hair from a human caused the potion to backfire and have unintended effects, because the Potion wasn't designed to be used to transform into an animal.
Her face was covered in black fur. Her eyes had gone yellow and there were long pointed ears poking through her hair.
‘It was a c-cat hair!’ she howled. ‘M-Millicent Bulstrode m-must have a cat! And the P-Potion isn’t supposed to be used for animal transformations!’
- Harry Potter and the Chamber of Secrets, Chapter 12 (The Polyjuice Potion)
The hair is what determines the form that someone will take when using Polyjuice Potion. It's one of the most important (arguably the most important ingredient) in the potion.
In Harry's first Potions class with Snape, we see such an example of a potion going terribly wrong because of a seemingly minor change.
“Neville had somehow managed to melt Seamus’s cauldron into a twisted blob and their potion was seeping across the stone floor, burning holes in people’s shoes. Within seconds, the whole class were standing on their stools while Neville, who had been drenched in the potion when the cauldron collapsed, moaned in pain as angry red boils sprang up all over his arms and legs.
‘Idiot boy!’ snarled Snape, clearing the spilled potion away with one wave of his wand. ‘I suppose you added the porcupine quills before taking the cauldron off the fire?’ Neville whimpered as boils started to pop up all over his nose. ‘Take him up to the hospital wing,’ Snape spat at Seamus.”
- Harry Potter and the Philosopher's Stone, Chapter 8 (The Potions Master)
The potion was one that was supposed to cure boils, but Neville Longbottom adding the porcupine quills before taking the cauldron off the fire caused it to melt a cauldron, burn through shoes, and make Neville break out in boils. A simple potion to cure boils, and keep in mind a potion considered safe enough to let first-years brew on their first day of Potions class, is certainly not supposed to have such explosive effects if brewed correctly.
The Dark Lord has some more relevant quotes in his answer that show the aftereffects of Hermione taking the Polyjuice Potion and how her return to human form progressed in the care of Madam Pomfrey.
The effects of the Polyjuice Potion with cat hair were already quite different from the intended effect, even without considering the duration it lasted. Hermione didn't turn into Millicent Bulstrode, or another human, which is obviously because the transformation is directly related to the hair used and no human hair was used in Hermione's dose of Polyjuice Potion to make that possible. However, she also didn't properly transform into a cat the way Professor McGonagall would when using her Animagus form. Instead, she turned into something with features of both a cat and a human, an odd mix between the two.
In addition, what also shows that it's only the use of cat hair that caused the potion to last so long is that Harry and Ron took the exact same potion at the exact same time as Hermione did. The only variable in their separate doses of potion were the hairs. Harry had Goyle's, Ron had Crabbe's, and Hermione had a cat's. When Ron and Harry took theirs, it worked exactly as intended, with no unusual effects, and it lasted for the usual amount of time. Hermione's dose of potion, however, turned her into a half-cat and lasted much longer than Polyjuice Potion is supposed to last.
