When Rory says it's too soon to kiss Jess in front of Doose's Market (because of Dean), Jess says, 'it's not the first time a couple has broken up' to which Rory replies, 'it is for us'. This is untrue; Rory and Dean broke up at the end of S1 Ep16 and didn't get back together until S1 Ep21.
Louise mentions that "one of the Manson girls" gets the trailer her family will be using after visiting her father in prison on Thanksgiving Day. Charles Manson is housed in California's correctional (prison) system, as are any of the women who were convicted for taking part in his killing sprees. None of them would be in a Connecticut jail.
In Doose's market, Lorelai observes that Kirk's basket contains Mercurochrome, which was taken off the US market in 1998.