Yep, it’s an episode of Gilmore Girls written by Daniel Palladino, so it’s time for another segment of “How to Make Sense of This Timeline”.
To recap. The episode begins with a Friday Night Dinner on February 7th, where Emily asks Rory to invite her boyfriend Jess to the next Friday Night Dinner, which would be February 14th. Sounds simple, right? Wrong.
The next scene appears to be the Sunday after the Friday Night Dinner, where Lorelai and Rory watch movies on the one day of the week they have to spend together. They discuss their future plans, which are that Rory is going on a date with Jess on the following Saturday afternoon, followed by studying in the evening, while Lorelai has a date with Alex at the same time.
Next, we cross straight to Rory and Jess’ Saturday afternoon date, which appears to be hanging around the town square together yet again. So … where did Friday go? That is, the Friday Night Dinner which was the day before this date?
The only way you can make sense of this is that Emily said next Friday, but she actually meant the next Friday to that, February 21st. As Friday the 14th is Valentine’s Day, it is possible that Emily gave them the night off from Friday Night Dinner so they could go out with their respective boyfriends. (There is precedent for Emily making allowances for romantic dates).
Therefore, the next Friday Night Dinner to February 7th would be February 21st, and this is the dinner Emily invites Jess to.
The Annotated Gilmore Girls 