Most do not sleep in the Sukkah on Shmini Atzeres because of concern that it would get in the way of enjoying the holiday which is technically a new holiday.
Some people do not eat in it during the night of Smini Atzeres but do during the day for the same rationale.
Some don’t all day for the same reasons.
An example that I’m surprised hasn’t come up yet for you, Ubi: Some people (namely Chasidim) are strict to never clap for applause on Shabbos, but when davening or singing Shabbos zmiros, it suddenly becomes magically mutar to clap and bang on tables. The Chazon Ish himself apparently denounced this one. I’ve never understood how this could have a halachic basis, but like DY said, we have to assume it does. If anyone knows the explanation I would be really interested to hear it.