While Archer hallucinates, his dreams recreate Heaven Can Wait (1978) starring Warren Beatty and The Natural (1984) starring Robert Redford.
The former dictator of Turkmenistan didn't, as Mallory claims, change the word for bread to name it after his dog. It was named after his mother instead. Other things Saparmurat Niyazov did during his time in power was outlaw beards, gold teeth, and lip syncing by singers. He also ordered that all television news readers should appear without makeup as they were supposed to represent the truth.
Archer references The Rat Patrol (1966) and its premise of chasing Erwin Rommel around Northern Africa and when hallucinating, encounters James Mason, who played Rommel in The Desert Fox: The Story of Rommel (1951) and The Desert Rats (1953).