One of my favorite things about the show is seeing different parent-child relationships. Lorelai and Rory have a very unique relationship, very different from Lorelai and her mother. They are often more like friends than mother and daughter, which is understandable given their relatively small age difference. After watching the first season (and almost the second), there are a few good things and a few bad things that the show portrays through their relationship.
1. Mutual trust makes for a much healthier relationship between a parent and child.
2. Both mother and daughter support and encourage each other. When something goes right or wrong for one or the other, they smile or cry with the other (Mosiah 18: 8-9 - solid Christlike principle!)
3. They spend a lot of quality time together which, from a human development perspective, is extremely important for adolescents.
Something I don't like as much, is a common issue in most relationships to some extent. Lorelai models a lot of immature and unhealthy behaviors and attitudes for Rory. While that is inevitable, I get bugged by it sometimes. That being said, I think there are more good things going on than bad. Sure, I don't agree with some of the things Lorelai does, but I think she is a really good mom and does a good job parenting.
From a critical media standpoint, I think it's a relatively good influence on its audience. But it's addicting and eats my free (and not so free) time, so it's sort of ruining my life. But at least I'm getting a good laugh!