One of my regrets for C++ is that it doesn't have interface checking when you instantiate templates. Coupled with the delayed instantiation (the code of a method is not fully type checked until you use it), static type checking of template code has been a hit or miss. Also, when you do get a type error, it is incomprehensible, riddled with the instantiation details that shouldn't be there in the first place. Interface checking means that the compiler can do better type checking before template instantiation. Interface checking has been in development for some time (e.g. Boost Concept Check, ConceptCpp, N2773), but it didn't make into the C++11 standard.
Interface checking in most programming languages follow a fulfillment model where an interface specifies a collection of function method signatures, and if a class implements all the functions (fulfills all signatures), then it is said to implement the interface. This is the case for Java and Go language as well as C++ concept checking in development so far.
However, if I were to develop interface for a new language, I would choose a declarative model where a class has to explicitly declare the interface it intends to implement. The interface is uniquely identifiable in the program's namespace. The motivation is to prevent a class from unintentionally implementing an interface by coincidence.
This is especially important for C++ since many operators are overloaded. For example, a random access iterator looks a lot like an integral type at the interface level (in fact it is a super concept because you can dereference an iterator), but manipulating the iterator like an integral without observing begin() and end() will cause the iterator to go out of bounds.
This semantic gap can be bridged by a more precise type specification using dependent type (not to be confused with C++ dependent type, a class that is complete if and only if a template argument refers to a complete type; complete type here simply means the compiler knows its memory layout so you can do a sizeof(type), for example, to get its size), but we don't yet have an object oriented dependent type system with interface checking. Even if we can bridge the semantic gap, I argue that a declarative interface checking is not less powerful than fulfillment interface checking.
Suppose you have a class Foo that implements all the methods required for interface Xyzzy, but Foo doesn't declare it so. In the fulfillment model, Foo can be used to instantiate any template (generic) that requires interface Xyzzy, but not in the declarative model, which requires Foo to explicitly state that it implements interface Xyzzy. Even if you cannot modify the definition of Foo, all you need to do is to subclass Foo and declare that it implements Xyzzy, and pass it to the template.
Another idea I have (in the context of C++ concept checking at least) is to get rid of the distinction between a class and an interface. Any class can be used as an interface. That's because C++ allows declaration and implementation to be separate. Furthermore, when a class is said to implement another class, it does not mean the class is a subclass of the other class. The compiler will only check that the method signatures are congruent.