I have a quite a few posts on Derrida and Heidegger here: I thought that I might want to highlight some of the more important ones for anyone who wants to understand what the two are up to. I don't mean to sound like an expert, but I do want to provide material for anyone who might find some particular formulation here helpful.
"Negativity, Repetition, and das Geschehen das Daseins:" what was for me (in writing it) an enlightening analysis of what Heidegger means by historicity and that enigmatic word in Being and Time, "repetition." I try to show that repetition here differs from the operation of the Aufhebung of Hegel.
"Building, dwelling, thinking...:" a close analysis of what is going on in "Building, Dwelling, Thinking," so we can understand the sort of linguistic work that is going on in Heidegger--what drives him to compose the way he does.
Then, three between Heidegger and Derrida:
"Time and Derrida:" a pretty clear distinction between time in Derrida and time in Heidegger (which can be calculated only non-properly or inauthentically). In Derrida we have a time that is to be calculated, but also flows confusedly (backwards as well, which, I maintain, is an unthinkable thought). This makes history seem very different.
"Derrida, Heidegger, Nietzsche, Sex," which looks at Heidegger and Derrida and their very different Nietzsches.
"Derrida on Heidegger and technics:" I read a little piece Derrida wrote on Heidegger, outlining one of his reservations in terms of Heidegger's conception of technics: Derrida thinks there need to be some changes in order for the technical and for the machine to be thought--despite the power and innovation behind one of Heidegger's most unique analyses.
"'By specifying 'If there is one,' recurrently:'" where I relate what Derrida is saying to Heidegger's economy of the same and Ereignis (enowning)--I recommend to anyone wanting to connect the two this way, by the way, that they read the little essay "Identity and Difference," in the small volume of the same name. Much will become clear. (One word of warning, though: this is not the only way to read Derrida.)
"Reading like Derrida, continued:" useful for the list at the bottom on what the text "is." I was trying to resist the notion that Derrida just close reads texts of philosophy.
"A few thoughts on 'Circumfession:'" I outline pretty clearly the problem of testimony in Derrida, illuminating perhaps how he conceives topics we would subsume under the name "ethical."
"Hesitancies:" My criticisms of Spivak's Derrida. I'd let up now a bit on the use of phase "desire for presence:" I do think Spivak misunderstands this phase, but I now see more of the necessity behind Derrida's use of it.
"Derridian dialectic:" I attempt to show that Derrida doesn't strictly oppose the dialectic. I would say now that he precisely tries to make it possible (which means making it impossible as such).
(I might also note that in "Criticizing (unlike) Derrida," I have what I think is a helpful formulation regarding Derrida and Foucault: it might be possible to see Derrida, not Foucault, as a thinker of institutions, and Foucault as a thinker of writing and texts. I don't really believe that wholly, but I think it's a neat way to begin to articulate reservations about Derrida, as well as begin to appreciate the strategic quality of his work: most notably the immense privileges that he bestows upon certain institutions and the immense criticisms that he levies upon others--though they are often also the same institution. Examples: psychoanalysis on the one hand, Marxism on the other. Derrida truly believes that psychoanalysis as an institution has a huge potential. Why? Because it is, as an institution, one of those that most tries to account for the violence involved in institution in the first place. This is why he will be fed up with those who take the institution of psychoanalysis--the notion that it exists or everybody knows what they mean by it and, most significantly, by its concepts--for granted: these people are erasing the instability, the ambiguity of its work of institution--what makes it, as an institution, radically resist being done with the problems of instituting or establishing itself. Marxism: here is an institution that also has a similar potential for radical resistance. However, it is also, more than psychoanalysis, taken for granted. The difference between how Derrida treats psychoanalysis--which, make no mistake, is very congenial--and Marxism--which is more reserved, more critical--indicates what are strategic decisions on his part and constitute his effort to be a thinker of institutions.)