What to do if a paper by respected authors has obvious problems, and I have told them so already?
Just a guess here, but I think you have done everything you can be expected to do and it up to the authors now. If they do something positive by your standards then all is well. But if they don't you aren't likely to get them to change unless they reach out to you in some way. 

You could, of course, produce a study with the correct methodology and attempt to publish it as a confirmation of the results of the other group. That is worth doing in any case. But how much you want to criticize the "respected authors" in your work is a judgement call that you should make only rather late in your process, not before you begin. 

I think that would be a good outcome for everyone, actually. 

But don't let the inaction of others frustrate you. It is out of your hands what other people do and going up against an establishment might not be a good career move. 



I'll add here that you might not be the only one to have informed them and that they are taking time dealing with it somehow. Anything from ignoring it to fixing it.