In Those Are Strings, Pinocchio (2003), Luke said they were visiting western Canada and then taking a cruise to Alaska. In this episode, he says they visited 7 countries on their cruise and also mentioned snorkeling.
When Jackson is going on his speech and says "if it's good enough for Rick and Dick, it's good enough for me," you can see Rory already has the button on in support, but he hasn't asked her if she wants a button yet or not.
When Rory is in Taylor's shop discussing her presence at the opening of his new shop, she says she only have a couple of days before going to Yale. However she does only find out after opening her mail at their home.
In English, "a couple of" can mean "two or three", but it can also mean the same as "a few" (an unspecified small number), especially if one wants the other person to think that this number is very low. Which is why Rory referred to the 9 days she had left as "a couple of days".
When Sookie opens her shed doors to show Lorelai the sex of her baby, you can see a hand in the bottom right corner reach and grab the door to keep it from bouncing.
Lorelai says that she and Rory got a train from England to Ireland. The two countries are separated by the sea and it would be impossible to travel between them by train.
The grand opening of Taylor's Olde Fashioned Soda Shoppe was supposed to be in May, but it was postponed because Fran died. It makes no sense that Taylor would wait all summer to have the opening if the shop was ready for business.