A general strategy you can try here is "respond to amateurism with professionalism".  Even if it looks like he's being unreasonable (as it currently seems to you that he is), just suspend disbelief, and, in a completely non-confrontational manner, engage his questions as if they were serious:

> I always appreciate constructive criticism [*true statement!  you don't
> have to say that his was constructive, let him think what he
> wants...maybe he actually did think it was*].  I didn't quite
> understand what led you to wonder whether I did enough testing of X. 
> Did you see something in the results that made you suspect this
> specifically?  Just want to make sure I'm not missing anything.
> 
> Thanks for your input!

Treat it exactly as if it were a sincere attempt to help, that you had a question about.  It's possible (though I'm thinking you think it unlikely) that he really is sincere and has something to offer you.  If so, wonderful!  You get useful feedback from someone smart!

If he doesn't actually have a real question, this technique may make that obvious in a relatively non-confrontational way.  Part of the value of it is that you are not simply being the victim of stalker-y behavior, but professionally and politely holding your ground.  It is to be hoped that this will lessen the feeling of exasperation that would otherwise normally accompany this kind of childish bullying, if that is indeed what it turns out to be.

There are very intelligent and successful people in academia who are nevertheless  woefully underdeveloped emotionally; one way this will be manifest is in the need to tear down other people who seem to be having success, or demonstrating skill, or garnering attention comparable to their own. This can catch one off guard when it's coming from a successful and respected person, because you would think that their success would be all they need to feel good about themselves.  That, alas, does not turn out to be true.  If it's a chronic emotional problem, you are unlikely to get him to change his behavior; hence the advice to concentrate specifically on blunting his ability to make his problem your problem.

If the cerebral approach doesn't work or becomes too time consuming, you can always set up a filter to send email from that address straight to trash....

**Escalation** (adding this section after your clarified and expanded examples indicate that mere polite discussion may not work here)

  1.  [Fuss level: zero] Gather evidence.  You don't have to do anything with it yet.  Later steps I will describe will talk about possible uses.  It's just good to have in case you ever get into a he said/she said situation and need to be able to back yourself up.

  2.  Note that there is already a "fuss", to some extent.  Not your doing.  You can't choose to have this situation be "fussless", because the behavior is happening in public.  The question is to what extent you wish to participate in the fuss.

  3.  [Fuss level: low] A body of evidence might be useful for you to have handy if you wanted to petition a site administrator to block him from contributing comments.  The sites hosting your research results and facilitating discussion don't want their work compromised by trolls.

  4.  [Fuss level: medium] Does he work at an institution with a published policy regarding academic ethics?  Spuriously calling into question the validity of your results seems like it would violate ethical standards.  It might be enough for you to obtain a copy of the institution's standards, highlight the part that you consider him to be violating, and send that information to him, asking for him to comment on whether he agrees his behavior violates those standards.

  5.  [Fuss level: high] Same as 4, but with more fuss.  Contact the institution.  Ask to speak to someone about the fact that you feel that one of their employees is violating academic ethics.  Do they have a published policy?  Can they send you a copy?  Can you send them some redacted examples and have them confirm that they would consider that in violation?  You would like to resolve the matter with the individual privately if possible, but you want to be sure that you are interpreting their standards correctly.  Then, email the stalker and tell them that you've been in contact with the ethics office, not having mentioned any names of course, we can resolve this between ourselves, can we not?, and they agreed that the behavior is in violation of standards.  Would he be willing to simply stop commenting on your work altogether in the future?  It seems it would be better for both of you if he did.  You don't have to threaten exposure--you should be careful _not_ to threaten, actually (to avoid any possibility that you could be charged with blackmail or whatever)--just state facts.

  6.  [Fuss level: nuclear]  Put all the evidence on the web, unredacted, and send a copy to his boss, his wife, and his students.  Let them know you really hate to bother them, but you need to ask them if they can contact his psychiatrist because he apparently needs his meds adjusted.  (<-- not a serious suggestion, but it was cathartic to type!)