My Review,
I really enjoyed it. I am going to focus on what episode 3-13 were like, because the first episode is a reunion episode, and the second episode is a bit transitional. The third episode is where the flavour of the new show starts to come out.
Overall, Fuller House has less of the formulaic stuff than that made up original Full House, although they do have homages from time to time. It still maintains some of the lame humour of prior show, but they merge it in with adult humour; other shows like Simpsons, Disney stuff, and Fresh Prince have done this sort of stuff. Speaking of Fresh Prince, there's one episode which has a particularly dark/emotional ending - Fresh Prince had one of these per season, and they were usually considered the best moments of the show.
On the characters:
Danny Tanner, Uncle Jesse, Uncle Joey, and Vicky have taken on a recurring character role. Danny is the typical father/grandfather type, he kind of reminds me of my father in law. Joey is the guy who babysits the kids from time to time. Becky is back and much improved over the original; she's funny now. Jesse is either a vampire, or they put him in a freezer during the 90s and just let him out now. Of the originals, Jesse and Becky feel like they mesh the best with the new show.
DJ (Tanner) Fuller is presented as the main character of the series, she's now a ~40 year old single widowed mother of three boys; pretty much the reverse of Full House. She tends to get the majority of the lame Full-Houseish jokes when Uncle Joey isn't around. She's a character with a comfort zone, and she gets frequently pulled out of it, and that is usually the conflicts in her stories.
Stephanie Tanner, in my opinion, is the standout character. She's come back after living the life of an independent woman, and has had some success. She's dabbled in sex, drugs, and rock and roll - which fills the position of Uncle Jesse from the original, but takes it in a different direction; a much sharper edge in my opinion. She's the source of many of the adult jokes, ranging from masturbation, to "deviant" sex stuff, and drugs; it's stated in the show that she at least is info marijuana. I think she's going to be the popular character of the adults on the show.
Kimmy Gibbler is Kimmy Gibbler, but now with alcohol. She has a much bigger role in this show.
Ramona and Jackson are both interesting characters in that they actually act like 13 year olds; which is different than the Simpsons/South Park trend where the children are not really children, but more like adults that have a child's avatar and live in a child's world; or Dawson's Creek where the teenagers all seem to have the attitude of pretentious middle aged women. They're actually very interesting characters with some funny stories, and the issues that seem relevant to them are similar to my younger siblings. They fit really well into the show.
Max is the competitive middle child, he'll probably turn out gay.
Baby Tommy is baby Tommy. He ages noticeably in the last few episodes.
Overall, I liked the show quite a bit. Much more than I thought I would since I really wasn't that big of a fan of the original series and it had negative reviews from most critics. I look forward to watching the second season when it's on, and I hope it's successful because I want to keep watching new episodes for years to come.