Should a move constructor take a const or non-const rvalue reference?

It should be a non-const rvalue reference.

If an object is placed in read-only memory, you can't steal resources from it, even if its formal lifetime is ending shortly. Objects created as const in C++ are allowed to live in read-only memory (using const_cast to try to change them results in undefined behavior).

A move constructor should normally take a non-const reference.

If it were possible to move from a const object it would usually imply that it was as efficient to copy an object as it was to "move" from it. At this point there is normally no benefit to having a move constructor.

You are also correct that if you have a variable that you are potentially going to want to move from then it will need to be non-const.

As I understand it this is the reason that Scott Meyers has changed his advice on returning objects of class type by value from functions for C++11. Returning objects by const qualified value does prevent unintentionally modification of a temporary object but it also inhibits moving from the return value.

Should a move constructor take a const or non-const rvalue reference?

It should take non-const rvalue reference. The rvalue references first of all don't make sense in their const forms simply because you want to modify them (in a way, you want to "move" them, you want their internals for yourself ).

Also, they have been designed to be used without const and I believe the only use for a const rvalue reference is something very very arcane that Scott Meyers mentioned in this talk (from the time 42:20 to 44:47).

Am I right in this line of reasoning? That I should stop returning things that are const?

This is a bit of too general question to answer I reckon. In this context, I think it's worth mentioning that there's std::forward functionality that will preserve both rvalue-ness and lvalue-ness as well as const-ness and it will also avoid creating a temporary as a normal function would do should you return anything passed to it.

This returning would also cause the rvalue reference to be "mangled" into lvalue reference and you generally don't want that, hence, perfect forwarding with the aforementioned functionality solves the issue.

That being said, I suggest you simply take a look at the talk that I posted a link to.