Rory is talking to Lorelai on the phone when she's in her dorm room. When she's sitting on her bed, the door to her room is closed. The shot switches to Lorelai then back to Rory, still sitting on her bed but with the door open.
When Doyle is finished handing out the jobs at the paper, he says "if you didn't [get what you wanted] I could care less". The correct phrase is "I couldn't care less". A skilled writer and stickler for perfection like Doyle would never have used the wrong expression.