Chacham Ovadia Yosef rules in Chazon Ovadia (p. 193) that it is permissible on Chol Ha'mo'ed to shower or bathe as one normally does, with hot water and soap. One may similarly comb his hair as usual on Chol Ha'mo'ed, despite the possibility that he will thereby detach some hairs. Chacham Ovadia also allows (p. 194) mopping floors on Chol Ha'mo'ed. In accordance with the view of the Shulchan Aruch (532), Chacham Ovadia permits nail cutting on Chol Ha'mo'ed, both on the fingers and toes. It is also permissible to polish shoes on Chol Ha'mo'ed (p. 195).
The Shulchan Aruch (535:1) writes that one may not move from one residence to another during Chol Ha'mo'ed, unless he moves from a rented residence to a residence that he owns. Even if one wishes to move to a more spacious and comfortable residence, he may not move on Chol Ha'mo'ed unless he currently lives in a rented home and moves to a property that he owns.
Although the Shulchan Aruch mentions a prohibition against removing refuse from one's home during Chol Ha'mo'ed, Chacham Ovadia (p. 196) rules that contemporary conditions are such that Halacha would permit removing the garbage from one's home to where it is collected by the local sanitation services. He applies this ruling even in cases where one is able to wrap and store his trash in such a way that it would not emit a foul odor. This is the ruling as well of Rabbi Yosef Shalom Elyashiv (contemporary authority in Israel), as recorded in the journal Mevakshei Torah (106).
Finally, it is permissible to prepare wicks on Chol Ha'mo'ed for candle lighting on Erev Shabbat and Erev Yom Tom (p. 197).
Summary: It is permissible on Chol Ha'mo'ed to bathe, shower, comb one's hair, mop floors, cut nails, polish shoes, remove the trash from one's home, and prepare wicks for candle lighting. One may not move into a new residence on Chol Ha'mo'ed, unless he moves from a rented home to his personally-owned property.
