I think that SBTB: TNC is unfairly slammed by many fans of the original show due to the fact that people who watched the original series and then TNC grew older and hence were more aware of the insane "cheese" factor that is a staple of SBTB. Let's face it, this isn't Emmy material by far. But it's still entertaining in its own right.
Although TNC's repeated cast changes confused viewers and stunted character development, they finally got it right in the end. One of the things I like about this cast is that the characters were not as confined to stereotypical niches like in the first show ("jock," "nerd" and so on). Each character has their own comedic and dramatic moments to shine. This allowed for a lot more flexibility with the characters to interact with one another and help each other out with the problems they face, as opposed to the original cast who was very clique-ish (i.e. the boys were off doing one thing and the girls another). However, I feel that many of the shows deliver the "moral" way too quickly at the end of most of the episodes. The lessons learned often seem rushed and forced by the writers and thus not very meaningful. I also don't like how Screech's continued downward spiral into a poor excuse for an Urkel impersonator hits its outrageous peak these seasons, even though it does make for some occasional funny material with Mr. Belding.
Furthermore, after 10 years of doing this show, its obvious that Bayside got way too small for them. Alternate settings such as the mall (where almost half of the episodes are filmed) and the police cadet academy (three episodes) just seem way to forced and take away from the original premise of the show.
This may be more attributed to the network or writers, but there are some obvious continuity errors in the sequencing of the episodes. Tony and Maria's relationship is off and on. They are dating in one episode and they have no scenes together in the next. Furthermore, DVD set also includes way too many "clip shows." Finally, the entire 4th disc chronicles their last days at Bayside leading up to graduation, which occurs in the 2nd to last episode, with the last episode on the disc being something random about getting ripped off by a mechanic. Compared to the original SBTB DVD's which had commentary, subtitles, a "Play All" feature, etc., this set seems very rushed.
But in the end, the show does its job. It makes younger viewers aware of the issues they face in adolescence and makes older viewers reminiscent of the good ol days.