Base-Breaking Character: Chachi-nated, or De-Chachi-nated? He was liked by fangirls for being a Mr. Fanservice and his relationship with Joanie, while other viewers found him an unnecessary addition to the cast with an annoying Catchphrase. Nick at Nite even made a marathon out of the "Chachi/No Chachi" premise, and viewers got to vote.
Broken Base: Despite being the Trope Namer for Jumping the Shark, a term that was coined when Fonzie jumped over a shark during Season 5, opinions widely vary among fans on when the show actually started going downhill. Some argue that the show went downhill as early as Season 3, when the show started being taped in front of a live audience. Some will say when Fonzie actually jumped the shark. Others will say when Richie and Ralph left the show after Season 7. A number of fans will even argue that the show stayed good for all 11 seasons.
Mork was only supposed to be a one-shot character and his episode All Just a Dream, but Robin Williams' performance was such a hit that the episode was revised to make the events real after all and gave him his own spinoff.
Before Chachi, in early seasons Fonzie had another younger cousin named Spike who completely disappeared after season 4. Chachi is introduced in season 5 in a similar role, but is eventually Promoted to Love Interest and ends up becoming a main character until the end of the show. It helps that Chachi was very popular with teenage girls and was also a different character from his cousin, while Spike just acted like a mini-Fonzie, even wearing the same clothes.
Arnold was the owner of the Drive-In in season 3, is replaced by Al in seasons 4-9, and eventually comes back after Al's departure in season 10. Both characters were well-liked and it's hard to tell which of them is more popular.
Replacement Scrappy: Roger, the nephew introduced after the departure of the main hero Richie Cunningham. Unlike adorkable everyman Richie, Roger is seen by most fans as a forgettable Flat Character.
Seasonal Rot: It started out as a very cool, low-key show, then became the ideal version of a standard sitcom with a Studio Audience. It started getting worse (the Trope-Named Shark-Jump) even before Richie left, but only got worse after that. Fonzie got a temporary full-time girlfriend for one season, and things got increasingly worse with gimmicks and nonsense until a thankfully fantastic final episode.