Saved by the Bell:
Zack's parents, go from divorced to married to divorced etc.
Not to mention Kelly and Jessie leaving for one season with no explanation, to be replaced by Tori. Who were replaced by Kelly and Jessie again, also with no explanation.
The show originally started in the Midwest, then moved to CA.
Family Matters:
The grandmother, younger sister, and aunt being written out without a reason. Yet they kept the aunt's son, never mentioning where his mother went.
Grace Under Fire:
Recasting the son from a short middleschooler to a really tall high schooler with no explanation.
The Cosby Show:
How did so many people fit in that house? I could never figure out where Theo slept since he was the only boy.
Night Court:
Dan's character going from sleeze to saint for one season really irked me.
As least they gave a reason (guilt), but it just didn't work.
All the different lawyers and characters the first and second season, never to be seen or mentioned again.
Facts of Life:
What happened to all the girls in the first season? It was still the same school, yet you never saw them again.
7th Heaven:
Is supposed to be set in California. When the daughter went to moved out with her husband, they said they could afford a house down the street. That street is very nice with big houses. The daughter was a college student while her husband was a police officer. How could they afford that in California?