How can there be a Saturday 6am breakfast crew if Luke doesn't even get there till 6?
In order to cook, prep must be done, oil must be heated (that takes a good 20 minutes), etc.
Also, when Lorelai forgets to paint with Luke, she is at the diner at 0615. The diner says closed - be back at 0600 (Luke says he is late, but the sign does say 6).
Doesn't he live there? Where is he late from? Why is he opening it from outside? Why is it already light outside?
So many issues...