This question has occupied my mind a fair bit. I think the best place to start is most definitely Latour's critique of critique. (This has been present in his work since at least 'We Have Never Been Modern' but has been most fully expounded in his essay 'Why has critique run out of steam?')
For Latour all critique, whether in the lineage of Kant through Marx to the Frankfurt School and today's poststructuralists or in the tradition of denunciation in the name of Science, results from the same ontological assumption: ontological un-flatness (what is the opposite of a flat ontology?). This is because critique is equated directly with denunciation and to denounce one needs an unreal overlaying the really real to peel back or tear away or unveil (postmodernists still follow this path even though they no longer believe in a real underneath the fabric - it's veil all the way down!). A flat ontology, for Latour, must therefore forego critique.
He makes a powerful point with regard to some elements of what has passed for critique to date. There is a widespread sense among (usually self declared) 'critical scholars' in the social sciences that not only is critique good but that it is the only valid occupation for a true scholar. All other forms of scholarship are seen as being somehow repressive. This is taken to an extreme by deconstructionists who insist that anyone enforcing their interpretation on anything is committing 'symbolic violence' or somesuch. To this extent, critique is a self-marginalising discourse. By this I mean that 'critical' thinkers are bound to ONLY criticise and they can only define themselves in opposition to a fabled 'uncritical' or 'essentialising' Other. For this reason they can never possibly succeed, which is a canny move as it means they never have to stop publishing and we never have to stop reading their work!
Latour makes mincemeat of these cliches but he goes too far. In fact I would say that he himself is too critical of critique - he ends up mirroring the very people he seeks to destroy. He has not one good word to say about critique and has no interest in asking what of it should be saved.
It's disappointing because Latour is at his very best when he takes something he disagrees with, takes it apart, translates it into his terms, puts it back together in the context of his overall system and makes you wonder how you ever thought otherwise. That is the way to proceed with the somewhat sullied word 'critique,' I feel.
informs me that 'critique' comes from the Greek kritikos "able to make judgments," from krinein "to separate, decide". The word thus carries connotations of separation and deciding; separation and judgement. Might we say that critique consists in separation and judgment? Judgement by separation? Separation by judgement? Aren't we all critically minded? If we weren't able to separate and to judge we wouldn't be able to get very far in life. If we accept something along these lines then there can be no more pure, exceptional form of critique only known by a chosen few (notice how in this way critique production has mirrored truth production
). If this is so then we have to distinguish between different forms of critique and separate the good from the bad (itself a critical act, as I would describe it). This would require no foundation (contra Habermas), it would proceed by a process of critical deambulation, if you like. This would be a better definition (if a broad one) because we wouldn't have 'critical' thinkers opposed to 'uncritical' thinkers and the self-perpetuating dance this necessarily creates.
(Also this is more or less what a music or movie critic does - breaks cultural objects down, analyses the pieces, relates them historically and contextually and judges them (or at least that is the ideal).)
Moreover, this definition wouldn't allow for the assumption that everyone is engaged in a competition to be more critical than everyone else. This is really what critique as a self-marginalising discourse must do - its a perpetual arms race, a race to the bottom that isn't there. No matter how critical you are I must always try to be more critical because that is all there is to do. If we try to do anything else we're committing 'violence' and so must surely commit hara-kari forthwith. As with all practices premised on fundamental bifurcations of reality, it just can't work.
Yet critique is far too valuable an activity to throw to the dogs of excess and stupidity. For all the negligence of those who take critique too far - and far away from where they should - they're not all completely mad - there really are those who would deny critique all licence as a scholarly activity. And these people are the real enemy.
Latour often goes on about how Science Studies was the only field that could foment the breakthrough of transcending bifurcated nature - in other words, refusing sociological idealism without trudging back to the same old realism; of forming a new realism. Science Studies, so he says, was uniquely placed at the midpoint of the 'two cultures' and he and others were thus able to realise how both sides had it all wrong. Well, I think something similar could be said for my field, International Relations, on this subject of critique. If eradication of critique is at all possible or desirable in Science Studies it certainly is not in IR, the field that deals with war, genocide, espionage and all forms of tyranny as a matter of routine. One would have to be an utter sociopath to engage seriously with these issues and not have some sort of 'will to critique' (although, having said that, there are plenty who would attempt to do so in the name of 'political Science', but that's another story).
So, I'm not sure what a flat ontological criticism would look like. First we'd have to figure out just what 'criticism' has meant in other traditions - it doesn't seem to be any one thing. I've been meaning to read Foucault's 'What Is Critique?' for a bit as well as Judith Butler's commentary on it. That might be as good a place as any to start.