Patrick Todd, Let's See You Do Better: An Essay on the Standing to Criticize, argues for the 'be better norm of criticism', which he formulates as follows:
One must: criticize x with respect to standard s only if one is better than x with respect to standard s.
Part of his attempt to motivate this is based on "Let's see you do better" cases, i.e., cases in which people respond to criticism by saying "Let's see you do better!" The whole argument is quite interesting. However, the 'be better norm' is, I think, obviously absurd and untenable, since it would require people not to criticize in cases in which we have good independent reason to think that people have a moral responsibility to criticize. For instance, you don't actually have to be better at politics than someone to criticize their political abuses, and any attempt to suggest the 'be better' norm in such cases would (I say) miss the point of such criticisms and, more importantly, the moral obligations that sometimes require that we make such criticisms.
It is true that people often try to evade criticism by pointing to hypocrisies and failings in their critics, but this cannot be regarded as good and rational behavior; it is often flailing and only really works to the extent that it appears to suggest that the criticism is a lying criticism. But the problem with a hypocrite pointing out your moral failings, if they really are moral failings, is not the criticism but the failure to apply it to themselves, as well.
In "Let's see you do better" cases, I don't think it's reasonable to see these as implying anything like the 'be better norm'; rather, the point is usually that the criticism fails to do justice to the difficulty of the task. In general, in fact, to a certain extent, "Let's see you do better!" acknowledges the criticism as to content; you don't say it if you can just point out that the critic is wrong. You do say it when you think the critic is underestimating the difficulty or complexity of the task being criticized, because difficulty and complexity are things that everyone thinks should be taken into account in evaluation. It's not the criticism but the glibness of it that "Let's see you do better!" highlights. This is the real reason for one of the features that Todd discusses, the fact that you can give the response on behalf of someone else.
I've sometimes commented on something like this with regard to 'mediocre' poets. Some people like to criticize poets like Alfred Austin as 'mediocre'. Austin is arguably not mediocre at all, and just labors under the difficulty of having been Poet Laureate immediately after Wordsworth and Tennyson, but even if he were, it's absurd to treat this as a serious criticism. The reason people make such criticisms is that they generally do not grasp the difficulty of poetry. To be even a mediocre poet is an extraordinary achievement; very few people make it so far, and a mediocre poet is going to achieve some very good work even if not consistently or with noticeable weaknesses. Thus if someone is being dismissed for being a 'mediocre poet', it's entirely reasonable to say to such a person, "Let's see you do better!" Underestimating the difficulty of the task being criticized is a common problem, in fact, in literary and artistic criticism, and it leads to distortions of judgment. Since literature and art are matters of skill, difficulty matters an immense amount in any reasonable assessment. Dante's Inferno is occasionally marred by pettiness and obscurity; this is definitely true, but let's see you do better.
When this is taken into account, I think it's clear that there's really no such thing as a standing of criticism, except in the metaphorical sense that if you criticize you should know what you are talking about; while it sometimes gets used loosely, 'standing' is really only relevant in matters dealing with harm, and honest and reasonable criticism is never a harm even when wrong.