Kyon is originally introduced in episode 4.19 as an exchange student, but in 6.19, Lane responds to Kyon's antics by saying "you're crazy! My whole family's crazy!" as if Kyon were a relative.
Mrs. Kim tells Lane to "take down the crucifixes" so that her Buddhist grandmother won't realize that they are members of the christian Seventh Day Adventist church (and indeed, a crucifix has been shown on the wall of Lane's room in the past). But, like most Protestant churches, the Seventh Day Adventists do not display crucifixes. Crucifixes (and religious statues) are mainly the domain of Roman Catholic practice. The difference between a simple cross and a crucifix is that a crucifix contains an image of Jesus on the cross. Most Protestants object to this, considering it a "graven image", the same reason they don't display statues in their churches.
At Lane and Zack's wedding reception when Rory is flipping through her pictures on her camera, Lorelai stops her and asks "Who's that?" and Rory responds that it's April. However, Lorelai met April previously and would already know who she is and what she looks like.
In the previous episode, The Real Paul Anka (2006), Mrs. Kim tells Lorelai that she was married to Mr. Kim 28 years ago. When Mrs. Kim has her sex talk with Lane, she remarks that maybe she will be lucky like Mrs. Kim was and only have to do "it" once. This would make Lane 27, but she is only 21.
Sookie is upset that the cookies for the bachelorette party gift baskets expanded and suggests that she may have put too much yeast in them. You do not, however, bake cookies with yeast.
Mrs. Kim sits down in the front pew on the right side, after walking down the aisle at the start of the church ceremony. The right side is traditionally the groom's side. Since Mrs. Kim is the mother of the bride, she should have been sitting on the left side of the church.
At Lane's wedding, Lorelai tells Christopher that Lane is the first one of Rory's friends to get married. However, in season 3 Dean and Lindsay get engaged, and subsequently marry in the 4th season. This would make Lane the second one of Rory's friends to get married.
Kyon says that there are two Mrs. Kims at the Kim's residence (Lane's mother and grandmother), but there is only one (Lane's mom), as Lane's grandmother is Lane's mother's mother and therefore, would not be a Kim.
In addition to this, we see Lane's grandmother leave immediately after the first ceremony.