The compiler generates code for calling the destructor after the object was moved. This was problem #1.
Regarding #2, take Resource Acquisition Is Initialization (RAII) as an example - in RAII, the existence of an object implies the existence of a resource. Now, if you want to be able to move, the object becomes "either the resource exists or it was moved out". As someone else noted in the comments, this affects not only the destructor. Methods cannot assume the existence of the resource, they have to check it first. Kind of like optional<MyResource>.
Regarding #2, take Resource Acquisition Is Initialization (RAII) as an example - in RAII, the existence of an object implies the existence of a resource. Now, if you want to be able to move, the object becomes "either the resource exists or it was moved out". As someone else noted in the comments, this affects not only the destructor. Methods cannot assume the existence of the resource, they have to check it first. Kind of like optional<MyResource>.