The iconic last cut in the opening credits for each and every season is an external shot of Luke's diner (we can see Lorelai, Rory, and Luke inside). This cut is from the last scene of the pilot. However, in the pilot, Luke's diner is a stand-alone building in the middle of a block on a busy street rather than a corner unit adjacent to the town square with windows facing in two directions and a door set in from the corner. The shot pulls back so that we can see the door and address. It can't be the Luke's we know from every episode after the pilot. The interior is a bit different as well.
The gender of Babette's cat "Cinnamon" changes. In the first season "he" gets stuck under Babette's porch and she borrows cooking oil from the Gilmores. Later on, the cat dies and "she" is mourned by many of the townsfolk.
Sets which should be somewhat permanent change, especially in early seasons. The foyer of Lorelai and Rory's house in S1 does not open to the living room, but it does for subsequent seasons. Luke's apartment changes frequently, with the bathroom moving from one side of the apartment in S1 to the other in S2. The cash register in the diner switches from one end of the counter to the other regularly in the first couple of seasons. The elder Gilmore's house changes as well. These are in addition to very large changes from pilot to series.
Lorelai's kitchen is on the right side of the house (when facing the house) with the door leading to the back. However, in nearly every external shot, characters who exit through the door come out onto the porch on the left side of the house.