Whilst Vala is cramming for her psych test she says "You see a tortoise lying on his back in the hot sun. You recognise his plight but do nothing to help. Why?". This is an abridged version of one of the questions asked whilst connected to a Voight-Kampff machine used to detect whether someone is a Replicant (a humanoid robot) in Blade Runner (1982).
Daniel Jackson makes a reference to one of the Knights of the Round Table from Camelot, Sir Gawain. Lt. Colonel Mitchell asks "Isn't he one of the Knights that says 'Ni'?" This is a reference to the Knights of Ni in the film Monty Python and the Holy Grail (1975).
Robin Mossley, who plays Dr. Reimer, previously starred in Window of Opportunity (2000) as Malikai, a man who tried using an ancient device to turn back time and in the process trapped O'Neill and Teal'c in a time loop.
Colonel Mitchel lists one of the drugs he receives from Stargate Command as 'dextroampheta-something'. This is dextroamphetamine aka pharmaceutical grade speed. This is a recreational drug (it causes euphoria) but it is also used by the US military to combat tiredness and fatigue.
This episode is about the team being afflicted by an unnatural sleep. The episode title alludes to this as Morpheus is the god of dreams who appears in Ovid's Metamorphoses.