Daniel has already linked to this video in comments, but I wanted to make an actual post about it:
The Husserl discussion here is pretty brief and not very revealing. Dreyfus, for one, is a Heidegger scholar and thinks that Husserl is only important insofar as he influenced Heidegger and showed (through his exemplification of it) the bankruptcy of a tradition going through Descartes and Kant, which entails starting your philosophical project with an analysis of consciousness and wondering how subjective consciousness can reach things out in the objective world when we think of or perceive or desire something. (More discussion of that issue is here.)
This characterization seems to miss the whole innovation of epistemology since Kant, which is to say that no, it's not that the mind is fundamentally divorced from the external world, but that in fact it constitutes the external world. It builds the external world itself. But of course, this picture is problematic: if "the world" is the world of our experience, i.e. is the result of this building process, then what about the building process itself? That would have to be somehow behind the world, its inner workings. But, really, there's no way we can know anything about those inner workings, because on this picture the finished building is all we can have any knowledge about.
So, post-Kantian philosophers like Hegel and Husserl throw away the idea that the world is a result of the unseen interaction between an ego and a thing-in-itself and instead focus on the world as we experience it, in which there do seem to be actors and acts and objectivity and truth and all the rest of it.
All of this gets worked out well before Heidegger, and I interpret Husserl in the Cartesian Meditations to be giving (like Heidegger does) a description that both describes this universe that's fundamentally unified with human understanding (meaning that there's nothing conceivable in this universe which we can't actually conceive, i.e. if it's not the sort of thing our minds can conceive, then we can't conceive it to exist) but which has the objectivity in it necessary to support scientific activity.
As discussed on our Husserl episode, the Cartesian Meditations is only Cartesian in that it starts with the idea that we need to begin philosophy by sitting back and observing our own consciousness to see what can be learned from it. Whereas Descartes thought he discovered indubitable propositions that could then be used to deductively prove the existence of minds and other people, Husserl finds a world of experience that, if interpreted without the injection of some kind of materialist or naturalist theory (which says that the objects we perceive are physical, outside, fundamentally different from us), leads us to see that the existence of the external world, other minds, and scientific objectivity are already indubitably certain to us: that we not only have no reason to doubt these things, but that the act of doubting them is somehow self-contradictory.
I'll admit that there's something unsatisfactory about this to me: Yes, my every experience presupposes a world of human meaning and an environment, so in a sense I can't "really" doubt these things, but Descartes is concerned with the logical relationships between these propositions (e.g. "there is an external world") taken abstractly; real doubt on the part of thinker, in the way I might doubt whether I really have my keys in my pocket or whether I forgot them, is not necessary. If Descartes can show that it's somehow interesting or relevant to determine the logical relationships between these propositions, like if we're trying to program a computer to simulate understanding and need to figure out exactly what explicit "beliefs" we need to encode, then it's a worthwhile project. The real force of the Husserlian (Hegelian/Heideggerian/etc.) argument here is that Descartes's enterprise doesn't really touch our experience as thinking human subjects; it's not going to tell us what we human beings should or shouldn't believe, because in effect, we have a bunch of beliefs (belief in the external world, in other people) just built into us and constantly reinforced, so maybe philosophy, if it's going to be more than just an academic exercise, has to do something else.
(I'll do another post on this series of videos when we publish the Heidegger episode.)