Let $Z=2^\omega$ be the Cantor space, $C(Z)$ the field of open-closed subsets of $Z$, and $RC(Z)$ the complete Boolean algebra of regular closed subsets of $Z$. It is known that $RC(Z)$ is a minimal completion of $C(Z)$.
I am interested in finding out more about the sets in $RC(Z)\setminus C(Z)$. I guess the simple answer is that they are precisely the regular closed sets which are not open-closed. Moreover, since every open-closed set is regular closed, and open-closed sets form a Boolean algebra, I can safely infer that the sets in $RC(Z)\setminus C(Z)$ are built out of infinite operations.
For example, let $\{B_i\}$ be an arbitrary family of open-closed sets. Then the the denumerable union $\bigcup_i B_i$ is open but not open-closed, and the closure of $\bigcup_i B_i$ is regular closed but still not open-closed unless ${\rm cl}\big(\bigcup_i B_i\big)$ is open, which is of course not true in general. Hence ${\rm cl}\ \big(\bigcup_i B_i\big)$ is an example of a regular closed set which is not open-closed.
(1) Are there other types of regular closed sets which are not open-closed?
(2) Also, are the sets in $RC(Z)\setminus C(Z)$ meagre?
Indeed a regular closed set $C$ is of the form $C= \overline{O}$ where $O$ is open in the Cantor space $Z$. As the clopen sets from a countable base for $Z$, we can write $O$ as $\cup_{ n \in \omega} B_n$, where the $B_n$ are clopen. So indeed $C =\overline{\cup_n B_n}$ or $C = \bigvee \{B_n : n \in \omega \}$, using the Boolean operation in $RC(Z)$, i.e. $C$ is the supremum of the clopen family. This observation is part of the proof that $RC(Z)$ is a (minimal) completion of $C(Z)$, namely we reach all elements of $RC(Z)$ as suprema of (of course at most countable, as $C(Z)$ is countable) families from $C(Z)$.
If $C$ is regular closed, so $C = \overline{\operatorname{int}(C)}$. If $C$ were meagre, then so would $\operatorname{int}(C)$ be (as a subset) and the only open and meagre set of $Z$ is the empty set, so then $C = \emptyset$. So all members of $RC(Z)\setminus C(Z)$ are non-meagre.