Stupidity: Richard, an insurance man drove Rory's Prius graduation gift to Chilton. The car wasn't insured, and presumably wasn't registered. An insurance man who is anal about following procedure drove an unregistered and uninsured vehicle? Richard wouldn't do it. Plus, Richard should have mentioned transferring the title to Rory. Can't insure it until it's in her name.
Stupidity: Rory arrives in Star's Hollow for the baptism. She parks presumably near the church. When she gets out of the car, she does not have a purse or car keys in hand. She apparently left the car unlocked and left the keys in it. It's just plain dumb.
Stupidity: Luke arrives at Lorelai's house. He comments that she left her car light on. Lorelai then tells him that she left it on because the porch light is out. He says that the battery is going to die. She tells him that she has it timed out perfectly. She then says that there will be 2 hours to spare and that the car has all day to charge. Cars don't charge unless they are running. Is she really going to run it all day? Why didn't Luke point out the error in her logic? Doing so is staying true to the character. The oversight is glaring.