When Rory sits at Luke's with Lane and eats the coffee cake that Luke has made for her birthday (and that seems to be too light to be a coffee cake), she, Lane and the cake are shown from different angles during their conversation. But the cake looks slightly different each time. Once there is a piece missing, but from another angle it is complete again. Furthermore the piece on Rory's plate enlarges while she watches Dean ordering coffee. It would not have made sense for her to get a new piece because she has hardly eaten anything, and the old one had still been on the plate before the camera swung away.
When Rory and Lane are eating coffee cake at the diner, the balloons disappear, then reappear, then disappear again.
Lighting flags are visible at several points, always on the left side of the screen. They can be seen when Rory is ordering pizza on the phone, very prominently when Sookie is in the Gilmore's kitchen and when Emily is looking at pens in the store.
It's supposedly Rory's 16th birthday in S1E6, but she's already driving solo in S1E4 when she gets hit by a deer. Connecticut requires you to be 16 to get a license.