I think Jon’s summary of the issues in chapter 2 is as comprehensive as it could be, considering the medium of our discussion, so my points here will mostly be related to things I’d like to reemphasize and draw attention to in terms of my own interests and my own reactions to the chapter. I wanted to post this immediately after Jon’s summary, but having gone through several reads of the chapter, I have continuously struggled to formulate my ideas as precisely as possible. So the resulting post is shorter and, hopefully, more concentrated. Plus, I of course got distracted and had to go look for my copy of Hermann Cohen’s Kants Theorie der Erfahrung because he was compared to Maimon in Atlas’s discussion of the latter’s theory of infinitesimals. [Cohen’s essay on Infinitesmal-Methode is available online] So, long story short, here goes.
As I previously stated, I find Kantian theory of sensibility/perception to be quite interesting, especially in terms of his understanding of space/time. I know that there are plenty of issues with it and I’m always excited about a debate, however something about his formulations vis-a-vis space/time being forms of intuition strikes me as if not solid, then certainly incredibly interesting, so my main interest in Chapter 2 is the business of the “infinitesimals of perception/extension” and Maimon’s original rethinking of perception as such, and consequently his rethinking of Kantian threesome of sensibility – understanding – imagination.
Differentials: infinitesimal of sensation/extension is like a geometrical point. This is not exactly how Maimon formulates his point in the very opening of the chapter, but I think it is useful to try and imagine it this way. What is so peculiar about a geometrical point? It is an ideal point, i.e., one cannot really point to a point and say “Here we have a point” (that is to say, of course, we can draw a point, but just like a drawing of a triangle and a triangle are not the same, so a drawing of a point is not really a point), and yet it constitutes lines and figures and so on. Maimon’s opening point is that we must think of perceptions as consisting of physical point (“differentials of an extension) that are, nonetheless, akin to mathematical points. I think this interplay between “ideal” and “real” is rather intriguing part of Maimon’s discussion of sensation/perception.
As Atlas notes in his chapter on “infinitesimals of sensation” (Chapter VI), Maimon does not really pursue this theory further in his later writings. What exactly is this whole business of infinitesimals and differentials? I think this is a larger question that deserves additional attention, but for now I just want to make some brief observations.
“The way objects arise” (mode of generation): new theory of sensation/sensibility. Maimon’s discussion of infinitesimals is a discussion of perception or “the way objects arise” – Atlas translates the first note [19/27] this way: “In mathematics as well as in philosophy infinitesimals are mere ideas; they are not objects but represent the mode of generation of objects, that is, they are mere limiting concepts, which we can always approach but never attain. They arise through a process of reduction ad infinitum of the consciousness of an intuition.” 
By rethinking what takes place in perception Maimon, in this sense, tackles the “myth of the given” from a rather original angle: infinitesimals as individual elements of perception are not given as such, yet they are there as the process of their unification in thinking creates/determines (“creates” is appropriate here, I think, but reads better if coupled with “determines”) objects. Atlas puts it this way:
“Sensibility thus furnishes the differential elements of consciousness; the imagination produces out of these elements a definite object of intuition and perception; and the understanding establishes the relation of the objects of intuition, i.e. the sensuous objects resulting from the integration of the various differential elements of sensation.” 
Compare with Maimon: “Sensibility thus provides the differentials to a determined consciousness; out of them, the imagination produces a finite (determined) object of intuition; out of the relations of these different differentials, which are its objects, the understanding produces the relation of the sensible objects arising from them.” [21/31-2]
It is in light of this articulation (much more nuanced, I think, in the text itself, even if somewhat confusing and all-over-the-place upon the first reading) that we need to take Maimon’s reformulation of noumena and phenomena.
Solution to the problem of quid juris: skepticism. The problem that Maimon encounters in Kant – how do pure concepts of understanding relate to intuitions/sensations – is solved by adding the new level of the infinitesimal elements. Here’s Atlas again: ” The pure concepts of understanding are not to be directly related to the intuitions, to the sensations, but to their infinitesimal elements, which are ideas of the generation of these intuitions.”  More precisely, Kant’s problem was, it seems, that we had to explain the relationship between given objects and pure concepts (roughly put). In Maimon’s articulation, the only “given” we have are infinitely small magnitudes that are not perceived directly as sensuous qualities of objects, but allow us to form objects through the process of unification we call “perception” – this is certainly an idealist position through and through. The relationship between “outside” objects and “inside” concepts is now a relationship between ideas. Where did thing-in-itself go then?
Rethinking noumena and phenomena. Probably the most interesting suggestion in chapter 2 is the following:
“[The] differentials of objects are the so-called noumena; but the objects themselves arising from them are the phenomena… These noumena are ideas of reason serving as principles to explain how objects arise according to certain rules of the understanding.” [21-2/32]
Thing-in-itself as a metaphysical entity existing before and outside of determined object of perception/understanding is a chimera. If Kant was ambiguous about it, then he shouldn’t have been, i.e., whenever he talks about it in a way that suggests its independent existence, he is wrong, according to Maimon (although he doesn’t quite put it this way, but we can help him here). Noumena are fictions that serve a purpose: to help understanding determine an object. The business of understanding is thinking, i.e. the production of unity in the manifold. Yet “understanding cannot think an object as having already arisen but only as arising” – sensibility provides infinitesimals, understanding provides a rule by which an object arises [22/33].
Concepts and intuitions (once more). There is an interesting couple of thoughts in Chapter 2 that pertain to the discussion of concepts and intuitions, especially in terms of illustrating Maimon’s general view of the matter. He uses the example of the concepts of cause and effect: “The concepts of cause and effect contain the condition that if something determined, A, is arbitrarily posited, something else that is necessarily determined (by means of the former), B, must be posted.” [29/46] This is how concepts works, and in this case, the concepts of cause and effect are posited in a way that establishes a necessary relationship between A and B. Now the real question is not whether the concepts of cause and effect are formulated correctly, but whether it is possible to see the fire burn next to the stone and, having touched the stone and discovered that it is warm, conclude that fire is a cause of the stone’s warmth. The question (at this point) then is whether I would ever even think of making the connection between sun and warmth were I not already equipped with the concepts of cause and effect? Where does the concept cause/effect come from? This is the key to Maimon’s skepticism (and his quid facti problem):
“Kant derives the concept of cause from the form of the hypothetical judgment in logic. But we could raise the question: how does logic itself come by this peculiar form, that if one thing a is posted, another thing b must necessarily also be posted?… We have presumably abstracted it from its use with real objects, and transfered it into logic; as a result we must put the reality of its use beyond doubt before ascribing reality to it as a form of thought in logic; but the questions is not whether we can use it legitimately, which is the question quid juris?, but whether the fact is true, namely that we do use it with actual objects.” [42/72]
In other words, to put it bluntly, the problem is not how we can legitimately (quid juris) apply the concept of cause/effect to fire and warmth (event A and event B), but whether our concept of cause/effect is truly an a priori concept and is not in fact based on the uncritical assumption that real objects already interact in some cause/effect fashion, assumption derived from simple observation of contingent events A and B (“subjective necessity (arising from habit) that is wrongly passed off as an objective necessity” [43/73])? To put it yet another way, the issue of legitimate application of a priori concepts to a posteriori intuitions takes the independent existence of both for granted while neither is really as obvious as Kant makes them out to be – the most important question here is the question of quid facti, not quid juris. This is where, of course, the ghost of Hume makes his entrance.
I have a heap of notes and jotted down observations still in front of me and I can hardly hope to go through all of them in order to address every single issue in Chapter 2 I found interesting, so the best strategy here is just to stop and press “publish”.