In the back of the limo, Luke says he hasn't been drunk in years; however he did get drunk in Season 4 episode 13, after an argument with Jess.
Sookie originally goes into labour just after Rory arrives at her house, so a little after noon. Lorelai calls Rory at approximately 11:50 the next day (specifically mentioned) and she says that Sookie had given birth to a baby girl following 14 hours of labour. According to the two previously given times it should've been 24 hours and not 14.