This is a bit old. But not the only problematic aspect of Kant's philosophy that I encountered after reading several introductions to his philosophy (from Stephen Korner's On Kant to several Stanford Encyclopedia entries), was his distinction between analytic and synthetic judgments, as admitted by the commentators themselves.
Analytic according to Kant is where the predicate "inheres" in the subject rendering the judgment true by definition. A synthetic on other hand is when the predicate doesn't inhere in the subject and therefore requires proof.
But the above theory is problematic at least in two respects.
First if our definitions follow the Aristotle's theory where concepts are defined by their genus and differentia, then any concept defined as such would have its genus and differentia "inhered" in it! So if you define a cat as "a carnivorous with ability for ambush or stalking and short pursuit hunting" (as per WP:Felidae) then all concepts used in the definition would "inhere" in it, and hence the judgement corresponding to it would be analytic by Kant's definition.
But this does not seem to be what Kant seems to have suggested by his definition of analytic judgement since he confines all analytic judgments to a priori.
However even with a priori qualification another problem rises which I call the phase problem of Kant's theory. This consists in the fact that once any empirical judgement is made, we no longer require an empirical investigation for expressing the same judgement afterwards, because then the same judgement would be ever true by definition which then leads to the first problem!
So we can conclude that Kant couldn't properly frame and capture his concepts of analytic and synthetic judgments. And this I read is widely acknowledge by Kant scholars. Coming from a background of acquaintance with Muslim philosophy I've found their logical and epistemological theories far more nuanced and sophisticated than Kant. However the Modern Analytic philosophy must have introduced many improvements to Kant's tradition.