Why an abstract class implementing an interface can miss the declaration/implementation of one of the interface's methods?

That's because if a class is abstract, then by definition you are required to create subclasses of it to instantiate. The subclasses will be required (by the compiler) to implement any interface methods that the abstract class left out.

Following your example code, try making a subclass of AbstractThing without implementing the m2 method and see what errors the compiler gives you. It will force you to implement this method.

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:)

That's fine. To understand the above, you have to understand the nature of abstract classes first. They are similar to interfaces in that respect. This is what Oracle say about this here.

Abstract classes are similar to interfaces. You cannot instantiate them, and they may contain a mix of methods declared with or without an implementation.

So you have to think about what happens when an interface extends another interface. For example ...

//Filename: Sports.javapublic interface Sports{   public void setHomeTeam(String name);   public void setVisitingTeam(String name);}//Filename: Football.javapublic interface Football extends Sports{   public void homeTeamScored(int points);   public void visitingTeamScored(int points);   public void endOfQuarter(int quarter);}

... as you can see, this also compiles perfectly fine. Simply because, just like an abstract class, an interface can NOT be instantiated. So, it is not required to explicitly mention the methods from its "parent". However, ALL the parent method signatures DO implicitly become a part of the extending interface or implementing abstract class. So, once a proper class (one that can be instantiated) extends the above, it WILL be required to ensure that every single abstract method is implemented.

Hope that helps... and Allahu 'alam !