I think the most unintuitive even unsettling aspect of entropy is that the entropy of black holes is proportional to their surface area, not their volume [0]. That is only briefly mentioned in the video and not discussed any further.
To be fair black holes are just weird so that's not too damning on its own.
What makes it weird is that black holes must necessarily* have the maximum amount of entropy for a specific volume. So not only the entropy of a black hole is proportional to its surface area, but the entropy of some volume of space can not grow beyond that. In particular entropy cannot be proportional to volume without limit, the density must be 0 on average for a big enough region.
The surface of a black hole is also the most efficient information storage possible - each 2x2 Planck lengths area can store a single bit. Of course there's no way to read that data...
What makes it weird is that black holes must necessarily* have the maximum amount of entropy for a specific volume. So not only the entropy of a black hole is proportional to its surface area, but the entropy of some volume of space can not grow beyond that. In particular entropy cannot be proportional to volume without limit, the density must be 0 on average for a big enough region.
*: According to some people anyway.