Taylor campaigns for sewers, but in Star-Crossed Lovers and Other Strangers (2001), Rory and Dean are walking through Stars Hollow talking about the Founders Firelight Festival and Rory says, "Last year we had a month-long carnival when we finally got off the septic tank system."
Richard is buried in a plot, but in Richard in Stars Hollow (2002), they talk about the family mausoleum.
Luke mentions he won't go to Woodbury for light bulbs, but the name of the neighboring town in the original series was Woodbridge.
During a brief shot of Lorelai's house at night, a whippoorwill is heard. Whippoorwills migrate south for the winter and would not be in Stars Hollow, CT during the winter.
In this chapter and throughout the mini-series, Rory is referred to several times as "32 years old". However, she would not turn 32 until October of 2016. So in Winter, it is only a couple of months beyond her 31st birthday.