These 5 shows were very popular (But how did their bad continuity impact the series?)
Riverdale
How could Cheryl and Jason be twins if Jason is the same age as Polly, Betty's older sister, but Cheryl is the same age as Betty? Although Riverdale attempts to suggest early on that Cheryl is older than Betty because how often is the captain of the cheerleading team a sophomore, ultimately, that suggestion was dropped and ignored fairly quickly in order to keep Cheryl around longer.
It would not be such a pointed continuity error had Riverdale decided to just make Jason be Cheryl's brother, rather than her twin. But, by constantly reinforcing the idea that they were twins, the only possible solution for the grade gap would be that Cheryl had been left back, except there is no evidence to that either, especially as Cheryl, as eccentric as she is, appears fairly academically bright.
FP's 50th birthday party also raises some eyebrows. During flashbacks, FP is referenced to be a teenager in the nineties, which would have made it impossible for him to turn fifty during the time of the show. "The Midnight Club" also suggests that Fred had given up music in his junior year when, earlier in the series, Riverdale had referenced that Fred and FP had been in a band together during their senior year.
The timeline itself also experiences continuity problems. When Jughead is attempting to fake his death in high school, Riverdale declares that it is 2020. The following season features a seven-year time jump, where the group has made it all the way to the distant future of 2021, or that is the year Veronica states it is.