The booing started as Palin was getting to her seat. You can see the surprise of Derek, Jennifer and Brooke, they had no idea what was going on "out there." It wasn't instantaneous with the score delivery, but seconds later. Something else was going on, and it happened as Sarah Palin was being led to her front row seat. It died down when host Tom Bergeron sat next to her to give her face time.
I wouldn't have booed her, but it was gross having her forced on us like that and it spoiled the show for many... check the twitter feeds. Viewers also had to sit through an interview at Palin's house in Alaska. Enough to make one gag. Tom DeLay didn't get this much time when he was a contestant and he was a personality in his own right, unlike Bristol, who only got the part because her mother is famous and divisive. (And Tom DeLay was personable and likable, despite his politics. Sarah Palin is not.)
The show is called "Dancing With the Stars" because the contestants are supposed to have been famous or infamous in their own right at one time. As Palin's partner said tonight, Pal