As I mentioned before, I'm leaning slightly against implicit interfaces, however, just to be thorough, I have to point out an argument in their favor.
Extension methods make it possible for Kotlin to add methods to existing classes without having to modify these classes. From this perspective, it may be reasonable to instruct the compiler that these extended classes now implement interfaces they didn't used to before. For example, if I add a "run()" method to an existing class, it would be nice to be able to tell the compiler "By the way, this class now implements Runnable".
This is beginning to look like Haskell's type classes, a feature that has many good properties.
Note that this suggestion is still not exactly an implicit interface, it's explicit but using the extension mechanism. Maybe the best of both worlds?