Perfectly fine.
You can't instantiate abstract classes.. but abstract classes can be used to house common implementations for m1() and m3().
So if m2() implementation is different for each implementation but m1 and m3 are not. You could create different concrete IAnything implementations with just the different m2 implementation and derive from AbstractThing -- honoring the DRY principle. Validating if the interface is completely implemented for an abstract class is futile..
Update: Interestingly, I find that C# enforces this as a compile error. You are forced to copy the method signatures and prefix them with 'abstract public' in the abstract base class in this scenario.. (something new everyday:)