It could be as minor as quietly asking a fireman to give him an alibi. Or asking the Fire Chief to lie and say there was training that weekend (in that first week after Suzanne disappeared, we know that Barry was living in his friend's house and that the Fire Chief was there often, as the Fire Chief describes Barry's behavior to a reporter).
Barry paced around a lot, staring out the window.
I believe that this type of murderer is super scared of getting caught, and that they (delusionally) want to turn back time and they hope that the dead person will somehow not be dead and the whole nightmare (that they planned and set up in various ways) will go away.
I think BM saw what he was doing as "setting up" or "playing around with" the idea of murdering his wife. I think he was deceptive with her about a lot of things and that she found out something major about him - something that will come out at trial and will shock all of us.