Mork says, "This is one of the old downtown hotels, Mind. You should see the ones on The Strip." This is a reference to Las Vegas, Nevada where the newer and larger hotels are on 'The Strip' (Las Vegas Blvd) and the older hotels are downtown.
Mindy says she is a stranger on a strange planet. This may be an allusion to the 1961 Robert A. Heinlein novel Stranger in a Strange Land, which centers around a vaguely Mork-like character. Mork himself recited the novel's title in Jeanie Loves Mork (1980).
When Mork is reciting a version of the Star Trek (1966) mantra, his "futuristic" sunglasses resemble the design which would later be used as Geordi La Forge's VISOR in Star Trek: The Next Generation (1987).