The cigarette in the ashtray has DISAPPEARED. The cigarette disappears and reappears as the interview goes on. Among the many hand messages Stuart is constantly sending there is a moment when he tells Jack about Charles Grady murdering his children and killing himself. During that part of his story he continuously points at himself with his thumb, sometimes covering it with his other hand and sometimes showing the pointing thumb (seen here). Incredibly, there is a miniature ax in the old English cup beneath the miniature American flag.

ULLMAN: '...he seemed like a completely normal individual (Stuart's pointing thumb is covered by his other hand)..he must have suffered some kind of complete mental breakdown. He ran amuk, killed his family with an ax (stuart uncovers his thumb, which he is pointing at himself)'.

If Ullman murderered the twins with an ax, it makes sense that HERE and HERE we find him saying 'goodbye' to sets of twins.