As much as I'm a fan of Heidegger and his project in Being and Time, I think he's critique of Descartes is off the mark, that is, outside of the broad critique that anyone can make of him.
First, the broad critique. Yes, indeed, the world is not divided into mind stuff and matter stuff. Now someone who subscribes to naturalistic inquiry will tell a certain kind of story about how the world is carved up and it won't be Heidegger's but let's leave it there. That is, in general, the broad critique.
Heidegger's specific critique of Descartes is that Descartes got us off on the wrong foot in his conception of us as self-possessed subjects over against objects. I'm no great lover of Descartes but this is unfair to Descartes. Descartes was not trying to capture our everyday phenomenological experience when constructing his dualism or conceiving of the world as a world of objects in view of subjects. He was doing two other things.
First, Descartes was trying to arrive at what's really real. Right or wrong, he thought how could do this from armchair speculation beginning with some basic assumptions and a simple kind of puzzle. The puzzle was, given the flux of all these worldly phenomena, what bit of the phenomena is beyond doubt? What couldn't be doubted, he concluded, was that he was a certain kind of perceiving being, one he called a "thinking thing." All right, and from there he got all his derivations.
Another thing Descartes was doing, especially after building up his philosophy from this epistemological foundation had to do with a number of tacit assumptions he was operating under at the time, a kind of mechanical philosophy by which everything in the world seemed to move through pushing and pulling. Well, in many respects this presents another kind of puzzle. If every bit of physics is a matter of pushing and pulling, how do we account for abstract stuff like ideas or intentions and a host of other mental phenomena that do not seem to have these push-pull properties? Another way Descartes fills out his understanding of ontology, then, is to conclude that the sciences deal with the push-pull stuff of matter, but the mind is very special because it doesn't have this mechanical nature.
What Descartes did not foresee and later thinkers dead is that he need not have posited nonmaterial phenomena, mind-stuff, rather he should have broadened his understand of what counted for material or physical, and that includes a broader category of stuff than that which has to do with contact mechanics.
The fact that Heidegger has Descartes saying that being a human is a matter of us just staring at stuff is laughable. It's a strawman. Descartes said no such thing and he has left us no such legacy. Never did.