I am currently in the process of reading Being and Nothingness. In the interest of getting through it, I have not been fully challenging Sartre's theory as I go along. Can someone point to the main objections to the philosophy in Being and Nothingness? Is Sartre's theory still "alive" or has it been effectively defeated in the decades since its publication?
Sartre's theory in Being and Nothingness isn't especially alive. There are several reasons for this. First, Sartre himself moved past his own theory in some of his later works specifically * Critique of Dialectical Reason* (which are by and large less read). I'm sure you can learn more about that angle in the entry on the Stanford Encyclopedia of Philosophy.
While I've read a decent amount of Sartre, I am most familiar with Part III ("Being for Others"). Here, there are several lines of critique. Sartre's account of how we relate to others is a dialectical approach which in some ways echoes Hegel. But there are elements of his account that are much more negative about human nature than Hegel's. For Hegel, everything will get better and we are meant for community with other humans. For Sartre, we're sex-crazed jerks who want to possess and control others, and the thought of being someone else's object is the most repugnant thing to us. But is Sartre right about this? His most compelling account is about a peeping tom who has the impression of being seen. But there may be other cases that are more appropriate for understanding how humans relate -- parents enjoying being looked at by their babies or such. He mentions this in a footnote explaining that his account presumes there's no possibility of good relationship with others.
Second, one could object to phenomenology more broadly and argue that it does not get us to the truth. Instead, they would maintain that we either need to switch to a hermeneutic method, deal with metaphysics proper directly, reduce everything to science, or be skeptical about any of these ideas. Sartre doesn't seem to have much arrayed against this. A further problem is that Sartre's dialectic is one that lacks the possibility of consciousness-together in a positive sense. In other words, it's Hegel stripped of necessity.
A third angle of objection is that Sartre doesn't contemplate a world with a prior relationship (God or the Other). This matters because if there is a relational God, then the relational system is utterly changed from his account. This objection's force is that if there's a consciousness there that should have priority over mine, then my weird resistance to getting along is kind of moot.