Re: Constructor
 
Eric l wrote:
    - Make all the constructors private and use factory methods,
      with the drawback that the class can't be extended.  (This
      approach avoids the quibble mentioned above, assuming the
      registration occurs in the factory rather than in the
      constructor.)
This is what I would do.  Bloch even talks about factory methods in Item 
1 of Effective Java.  I think there aren't enough folks using factory 
methods if he puts it as #1.  They can be clumsy to work with, and seem 
un-OO, but factory methods are a great pattern and should be used more 
(when appropriate, of course).
I wonder if providing an abstract class to base future classes on would 
work, if extension is important.  Hmm, but it would be possible to use 
the class outside of the factory method.  Documentation might work 
here... so might relentlessly testing each object passed in to make sure 
it was registered.  A clever design might even eliminate most of the 
overhead by only checking on a few critical methods.
I guess you could call your base class the "implementation" class, then 
use a restricted wrapper to get the real object to work on.
public abstract class Implementation {}
final public class Wrapper {
   Wrapper( Implementation i ) {}  // package private
}
public class Factory {
   private Factory() {}
   public static Wrapper getNew( Implementation i ) {
     Wrapper w = new Wrapper( i );
     Registry.register( w );  // not shown
     return w;
   }
}
So if all your methods require a Wrapper, the compiler does the checking 
for you.  This also seems Dependency Injection-y, which might be a good 
thing.