The fact that Andrew leaves out what the man said about Jay possibly being "crazy drunk" is significant to the suggestion of alcoholism that hovers in the background throughout the story. Andrew knows that Jay used to have a drinking problem, and he does not want to even suggest to Mary that drink could have been the cause of the accident. The narrative never resolves this uncertainty, as we never find out whether Jay was drunk at the time of the accident.
Hannah goes to Mary and tells her it is only natural to grieve, and that she must stop asking God's forgiveness for doing so. It is good that Hannah intervenes, as she is the only other religious person and therefore probably the only one Mary would listen to on that point. Their conversation demonstrates once again how alone the two women are within their family in terms of their religion. This divide is again emphasized when Joel makes the comment about how the gods kill humans "for sport" (a quote from Shakespeare's King Lear) and Mary protests. Joel tries to hold himself together, but thinks, "If she tries to tell me it's God's inscrutable mercy, I'll have to leave the room."
The family's laughing fit is a point of relief for us in the narrative and for the characters within the plot as well. Though they all know their laughing is inappropriate, none of them can stop because they are in such need of the comic relief. The family's hysteria highlights how awful the situation is: nothing at that point is truly funny, so they cling to the one funny occurrence—Catherine's comment—and wring an inordinate amount of humor out of it.
At the end of Andrew's story, when Mary asks Andrew to phone Jay's family, he asks her what the phone number is. She cannot remember it, which makes her feel guilty. She says that Jay was always the one who called. The fact that Mary has never called her in-laws herself is another subtle hint at the tension between Jay's family and the woman he married.