As with so many episodes written by Daniel Palladino, I cannot follow the timeline of this episode very easily. It opens early in the morning, and we know it’s a school day, because Rory is dressed in her Chilton uniform. Yes, she has to get a bus to school, and they can’t go to the diner, so it makes perfect sense for them to walk a long way for a friend to cook them breakfast! They really should have just made their own breakfast, for practical reasons.
However, the next few scenes have Rory dressed in her normal clothes and Lorelai isn’t at work, so that it seems to be the weekend. That implies they had breakfast at Sookie’s on a Friday morning, but the previous episode ended on Friday night. And they can’t have skipped a week, because Rory was meant to have her cast removed in two weeks, so it would have been gone by that time.
I think just as “PS I Lo … ” has two Thursdays in a row, there are two Fridays in a row as we transition from “Help Wanted” and “Lorelai’s Graduation Day”.
The timeline issue could have been fixed by simply making their breakfast on Saturday morning, which makes sense because they always eat out for breakfast on Saturday, and they would have plenty of time to walk to Sookie’s (and Lane would have the free time to practice drumming on pots and pans). It would even make it slightly more plausible that Jackson was sitting around in his PJs and not at work.
Possibly the problem isn’t the fault of the writer this time, but of the costume department, for putting Rory in a school uniform she shouldn’t have been wearing. The only way I can make sense of this is for Rory to have run out of clean clothes and forced to wear her uniform on a weekend – or she has some school activity that Saturday, like a debate, and is already dressed for it.