When the reverend is speaking and Kimmy imagines his face to be upside-down, the movies he mentions are The Sixth Sense, The Village, and The Happening. All three of those are movies by M. Night Shamalan
Keith's uniform tells a very interesting (and plausible) story, if you know how to read it: he is a member of either the 75th Ranger Regiment or the Ranger Training Brigade of the US Army (Army Class-A uniform, tan beret), has been wounded in combat (Purple Heart), served in both Army and Joint organizations (Joint-Service Commendation Medal, Army Commendation Medal, Joint-Service Achievement Medal, Army Achievement Medal), demonstrated good conduct throughout his career (Army Good Conduct Medal with Bronze Knot device), enlisted before November 30th 1995 (National Defense Service Medal with one Bronze Campaign Star), is probably a veteran of Somalia (Armed Forces Expeditionary Medal), is a veteran of Kosovo (Kosovo Campaign Medal), Afghanistan (Afghan Campaign Medal with Bronze Campaign Star), and Iraq (Iraq Campaign Medal with Bronze Campaign Star) with at least one additional tour in either Afghanistan or Iraq (Global War on Terror Expeditionary Medal), and at some point served as a UN observer in Egypt (Multinational Force and Observer Medal).
Both Ellie Kemper and Sam Page attended Princeton University.
Sam Page played Greg Harris, a failed doctor who joins the military, on Mad Men.
When Dierdre (Anna Camp) challenges Jacqueline (Jane Krakowski) to unseat her as Alpha Mom (at the 13:35 mark), she quotes a line of poetry, "How dull it is to pause, to make an end, to rust unburnish'd, not to shine in use!", from the poem "Ulysses" by Alfred, Lord Tennyson, written in 1833.